I've been doing a pretty intense programming sprint for the past few weeks, and my directive is to hack in a complicated feature into a big legacy code. The directive is to make it work, quickly, and don't worry about polishing it up or making it fit existing standards.
Of course, if you've ever written a lot of code, you know that doing the same thing in a lot of different places the same way introduces a whole lot of extra effort. If I found I did something wrong in one of these duplicated code sections, I have to remember to change all of them. And if I forget one or two or many, I will think my corrections didn't work and spend a lot more time trying to figure things out...
I bring this up because it's a useful analogy and not because I've spent the past 2 weeks trying to fix something when it turns out I forgot to put a change in all places... yeah, let's stick with that story.
If I took the extra time up front to make sure duplicate code is put into a single place and referenced where needed, then I just have to fix one thing. And I'd be a lot less frustrated trying to make progress.
Duplicate questions with duplicate answers have the same potential for regressions. One question (Question B) gets closed as a duplicate of another (Question A) -- this is the system working to "refactor" things into a single place. But duplicate answers are not directly linked to each other. If an answer on Question A is updated, revised, improved... that does not change the form of the answer on Question B.
This introduces a regression. A user can arrive at Question B and see the answer as well as the duplicate banner, then go to Question A and see a similar-but-different answer from the same user. Maybe they check time stamps and put together what might have happened, but that's pretty unlikely. So instead, they ask yet another question (Question C) that says:
I read Question A and Question B, and they are identical, yet their answers are slightly different. Which one is the true answer?
And now we've made a mess of things. For all we know, Question C collects a different set of answers that are distinct from what is on A or B and now we've failed at creating a definitive, high-quality question-and-answer site. Instead, we have different answers to the same question spread across multiple places.
Instead of letting that happen, deleting the answer on Question B makes it clean. Question B is closed with a link to Question A, and Question A contains all of the answers. In addition, as rob discussed in his answer, deleting the answer means Question B can be edited to make it distinct or it will be removed over time because it is abandoned -- again, making the site cleaner.
So what is the preferred course of action? We want all of the answers on Question A and any duplicates of A should not be considered source material. There is a moderator tool that can merge questions together. This would have taken the answers from Question B and moved them to Question A and preserved rep gained/lost for the people who answered the question. The way to ask for a merger is to A) Vote to close as a duplicate and wait until that is done, and B) Flag the question and explain why it should be merged with the duplicate.
That sounds pretty great, so why don't we do it that often? Well, the advice I often see from other moderators and community managers is that merging is messy. If something goes wrong, it's not trivial to unwind the mess and get things back to the way they were.
Furthermore, merging the question, especially if it happens right after it is closed as a duplicate, prevents OP from editing their question to make it distinct. They would instead go ask a new question that they think is distinct. Minor burden perhaps, but the people who ask 100% identical questions to others on the site tend to be new, whereas people who would know to ask for a merger tend to be established -- I would rather see OP learn to edit their questions than to get into a habit of re-asking the same thing when their original is closed.
All that is to say, for easy-to-copy answers on identical questions, if somebody asked for a merger right after the question was closed as a duplicate, I would probably just suggest they post their answer on Question A and delete it themselves from Question B. Sure, they lose a little rep on Question B -- but posting the answer on Question A bumps it to the front page and if the answer is good, they should get the rep back (and possibly more). And it's a safe, clean way to do it where if something goes wrong, we don't need CM/database developers to fix it.
And it prevents divergence leading to regressions and follow up questions about why there are different answers.
The ideal use case I can see is when we have Question A with many great answers, and then Question B is posted and although Question B is a duplicate of Question A, let's say that Question B is a much better question. We want the best questions with the best answers, and so in that case it might be worth closing A as a duplicate of B, even though B is newer. Then it might be worth merging the answers from A into B. But this is a pretty rare thing and we'll cross that bridge when we get there.