england-and-wales
The non-pecuniary losses a claimant suffers are indeed difficult to assess for the reasons you state. The impact will mean different things to different people, depending on their sex, age, hobbies, etc. As you speculate, precedents are particularly important, although this is complicated due to the range of relevant factors listed non-exhaustively above. As such, practising lawyers will often consult specialist texts and guidelines to determine the range of possible damages.
I will now use the example of personal injury (which includes psychiatric injuries) to make this more precise.
Note 1: Everything below relates to a combination of the subjective pain, suffering, and loss of amenity experienced by the claimant. This does not include any objective costs (in line with what your question asks for; these pecuniary damages would be awarded separately from what is discussed below).
Note 2: The principles from below illustrate how non-pecuniary damages are calculated. Similar texts will be used for other types of harm (eg other emotional distress, invasion of privacy, etc.)
Personal injury lawyers refer to practitioner texts (such as Kemp & Kemp: Quantum on Damages) and the Judicial College Guidelines for the Assessment of General Damages in Personal Injury Cases. The former usually contain the facts of thousands of personal injury cases and the damages awarded. The latter contains the usual range of damages awarded for non-pecuniary losses in personal injury cases based on the type of injury and the severity. Of course, I have just used personal injury cases as an illustrative example. Similar texts are available for many other cases.
Using an example, let's say that the victim of a workplace accident ("Bob") has:
suffered minor PTSD
with treatment costs of £3,000
and £5,000 of lost income due to a temporary inability to work.
If his claim is successful, he will be entitled to the combined figure of £8,000 of pecuniary damages plus any non-pecuniary damages. These can be found using the Judicial College Guidelines (10th edition), which suggest he would ordinarily be entitled to an additional £2,600-£5,400 for minor PTSD. However, on more facts, similar cases could be found in Kemp to clarify the exact figure.