Can poetry be substantively conducive to philosophy?

Yes.

For example Friedrich Nietzsche wrote over 400 poems, many of which were expressions of philosophic views.

Thus Spake Zarathustra was a sort of prose–poetry.

And in The Birth of Tragedy, he assesses the philosophical value of various kinds of art, including poetry.

Poetry is a matter of form. One can write very direct poetry; one can write very elliptical prose.

Elliptical prose can be a way to provoke thought. Zen koans would be a good example of trying to encourage and direct the audience to explore philosophical ideas.

Direct poetry can simply be a challenge that the writer has set for themselves, or another way to make written ideas more memorable and engaging, or may just be a way of showing off language skills. Lucritius' magnum opus, as I understand, is a prime example of direct poetry which covers a lot of philosophical ideas. (I have read about it, I have not read it yet.)

The problem is, it is hard to write good philosophy, it is hard to write good poetry, and the two challenges multiply rather than add. Good philosophical poetry of more than minimal length or minimal ideas is a major challenge. Weaknesses in either can annoy the audience enough that they stop reading or listening. People are more tolerant of weak prose if it contains good ideas then they are weak poetry, which can come across as pretentious or simply bad judgment.

"When it is good it is a very very good, when it is bad it is horrid." And even moderately good is hard.

(The same kind of conflict can arise when trying to write science fiction mystery stories, or any other crossing of genres that each have strong rules for what is and isn't appropriate in that kind of story. It is much harder to do a good job of meeting two sets of criteria at once then of meeting them independently.)

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Re storytelling with strong exploration of philosophical ideas: I admit to being a fanboi (it is probably a good thing I know I'm not her type), but I still think Ada Palmer's "Terra Ignota" quadrilogy should have won the Hugo award both times it was nominated. Superb writing and world building, and the explicit philosophical material is well integrated and advances the story. Not, I will admit, an easy read but a highly engaging one. And it successfully does the interdisciplinary dance. Wow.

I haven't heard of poetry being part of the syllabus of a philosophy course. It does get mentioned in critical thinking/logic courses as a fallacious mode of thought viz. appeal to emotion.

Jokes however are a different story. Wittgenstein is supposed to have said that philosophy can be taught/learned as a series of jokes. Everyone's heard of Socrates' 3 tests joke.

However poetry has a way of connecting directly with the "heart" and people may confuse rhyme for reason.

There is a Nobel prize for literature, but none for philosophy. There are various less well-known, much less prestigious prizes for various forms of philosophy, of course, but I cannot, off the top of my head, remember any.

Poetry and imaginative literature are ways to amuse ourselves, but also ways to find ourselves. That is, to find out on an affective, personal level who or what we are, to exercise our imagination, and in particular, exercise empathy. In Aristotle's poetics dramatic (enacted) poetry can effect a catharsis, a clarification and rebalancing of our emotions. Strictly discursive, argumentative prose doesn't do this and cannot do this -- though some forms of discursive writing lean more heavily on metaphor or on lyrical personal expression. (For instance, certain passages in the Myth of Sisyphus or Emile Cioran's outbursts. It's no coincidence that these are existentialist writings.)

If we just want to be informed about facts, poetry seems (at best) a frivolous, useless distraction. Perhaps a kind of ornament. Pretty words. Clever puns. In the words of Droogstoppel, the dry, unimaginative, judgemental coffee broker who is one of the main characters in Multatuli's novel Max Havelaar:

Sedert jaren vraag ik mij af, waartoe zulke dingen dienen, en ik sta verbaasd over de onbeschaamdheid, waarmede een dichter of romanverteller u iets op de mouw durft spelden, dat nooit gebeurd is, en meestal niet gebeuren kan

For years I have asked myself what such things [poems, plays, fictional stories] are good for, and I am astonished at the shamelessness with which a poet or novelist dares to spin you something that never happened, and in most cases never could happen.

But facts as such are meaningless. The facts never "speak for themselves". To express what something means we need other forms of language too - and we need an open-ended context in which language can be used in play, that is, in ways were we must not always mean what we say.

The most important modern philosopher who suggested that poetry could express something important that can not otherwise be expressed is Heidegger. In his later work he called language "the house/home of being" (das Haus des Seins). Poetry allows us to dwell in that house.

The most important ancient philosopher who suggested something somewhat similar was, in my opinion, Confucius. Confucius himself, according to later tradition, spent a lot of time compiling the classical Shi Jing (The Book of Odes or Book of Songs). He regarded memorizing and understanding the odes as extremely important for cultivating moral sensibilities, and basically, to become a fully accomplished human person:

The Master said: "Stimulated by the Odes, standing firm by the Rites, coming to fullfilment in Music" (Analects 8.8)

There are at a minimum truths that are, for some people, more easily understood through fiction than through rational argument.

It is not clear whether there is any truth that poetry could reveal that could not possibly be revealed through rational thought and pure reason. But that is an extreme.

There are absolutely things that can be revealed more intuitively and in a fashion that is easier for at least some people to understand through poetry and literature than through rational thought.

Parables often depict ethical and religious thoughts more clearly than an academic theologians arguments do. I found many of Oscar Wilde's poems and stories to present many ethical thoughts in a way that was easier to understand than those same ideas presented as rigorous ethical arguments.

Many political sentiments are expressed through fiction in ways that can be more persuasive than if put into formal argument. George Orwell was famous for this with 1984 being his most famous work, though examples of works that deal with politics through fiction are absolutely legion.

I suspect there is no truth in poetry or fiction that could not possibly be discovered or expressed through coldly rational argument, but there are many things expressed in them that would be difficult to put into a rational argument and are (at least for some people) more easily understood through poetry and fiction.

I see a number of ways in which poetry and literature (as you allow in the question text), or in a broader sense any artistic form, can at least help to gain philosophical insights.

• Ethics is ultimately informed by and aiming at reality and our actions in it. In its function as "make-believe reality", literature is an interesting device to broaden our horizon, increase our slice of perceived reality. It allows the reader to put themselves in the protagonists' shoes in a way they otherwise may never experience. This "seeing the world from a different angle" is the key element and motivation for developing morality and ethics; if we were only concerned with ourselves, we wouldn't need any. We have these "mirror neurons" that make us feel what others feel. Perceiving how it feels to be at the receiving end of an action may lead to a different assessment of that action, more so than an abstract discussion.

• Literature can provide specific examples of ethical dilemmas that may prove or disprove the validity of the relevant ethical standards. Casuistic arguments are one classical part of the philosophical discourse. Adding emotion to such an argument, as the literary form typically does, makes it more effective.

  Dostoevsky is one of the most famous and influential authors who explored morality in his work.

  Philip K. Dick wrote a story in 1974 in which he imagined that the time limit for legal abortions would be an arbitrary 12 years after conception, instead of an equally arbitrary 3 months, making a strong argument against any such limit.

  Rashomon, a film by Akira Kurosawa based on the story of the same name, became the namesake for the "Rashomon effect": "The naming of an epistemological framework — or ways of thinking, knowing, and remembering — required for understanding complex and ambiguous situations."

• The special literary form of poetry can lead to philosophical insight because of its typical brevity. In the spirit of Shakespeare's self-referential "brevity is the soul of wit", let me quote the Austrian poet Erich Fried:

  Wer will
  dass die Welt
  so bleibt wie sie ist
  will nicht
  dass sie bleibt
  

  (Those who want / the world / to stay as it is / do not want / it to stay)

  In this dialectic contradiction we hear our Heraclitus and his descendants; we understand that the world is a process, and stagnation the process's end, and hence the world's; that progress is an inherent trait that must be embraced; and we hear the urgency (the poem is from 1983) of an impending peril commanding action.

  Due to their brevity, poems offer themselves up to interpretation; they serve as a nucleus around which insight can aggregate, through imagination, association and reason. Poems thus can serve as a sort of "philosophical catalyst".

Please don't laugh, everyone, but I just did an experiment by asking an AI (Gemini 3) to write a poem in the language of Wittgenstein about the philosophical meaning of ice cream sprinkles. The result is obviously a random deformation/imitation of Wittgenstein's language. You can judge for yourself if Wittgenstein's method survives the experiment. Not only do I think that it does, but I think that this makes him much more relatable to the casual reader. I find myself putting up way less resistance to his ideas after seeing his language applied to a silly case. Did such "poetry" (no matter how bad) conduct me to serious philosophy? I believe so. Anyway, enjoy or be appalled:

"The Tractatus of the Confectionary Dust

The world is all that is the case, yet the case contains the ice cream. The boundary of the bowl is the limit of the philosophical investigation.

I. The sprinkles, die Streusel, are not the ice cream, nor are they the flavour of the ice cream. They are an adornment. The sprinkle is a sign for the possible state of affairs: dessert completed.

II. The proposition is a picture of reality. The sprinkle is a picture of frivolity. When I say, "I desire the rainbow sprinkles," this is a meaningful utterance only if the state of affairs rainbow sprinkles on cone is conceivable. But the rainbow sprinkle (Jimmies) and the chocolate sprinkle (Nonpareils) exist in two distinct logical spaces.

III. To choose the chocolate is to assert the uniformity of the aesthetic field. It is a statement of metaphysical conservatism. The form of the picture is its possibility of showing how things are related. The chocolate sprinkle relates only to the monochrome universe.

IV. To choose the rainbow is to embrace the contingency of experience. It is to accept that the logic of the confection does not necessitate one colour, but all colours simultaneously. What can be said at all can be said clearly; and whereof one cannot speak thereof one must be silent. Can one speak clearly of a rainbow sprinkle? Only by enumerating its distinct atomic facts: red, orange, yellow, blue...

V. The problem is not which sprinkle, but that the act of selection itself presupposes a criterion of value. If I select the rainbow, I do not merely state a preference; I assert that colour variety is a property of the good dessert. The ethical is transcendental. The aesthetic, too, is transcendental. The sprinkle choice is a boundary condition on the will.

VI. The limits of my language mean the limits of my world. The limits of my available sprinkle types mean the limits of my culinary freedom. If only the vermicelli are present, the question of the jimmies is unaskable. The correct sprinkle is the one that allows the sense of the ice cream proposition to be truthfully represented.

VII. Wovon man nicht sprechen kann, darüber muss man schweigen. (Whereof one cannot speak, thereof one must be silent.)

Let the perfectly correct sprinkle be applied, and let the spoon commence. The meaning of the dessert is in its consumption."

Yes. Such can be found in Zen

Dig a hole for your pond without waiting for the moon. When the pond is finished, the moon will come by itself. - Dōgen Zenji