No. I think that in general, we should never re-tag based on answers.
Tagging based on answers has, among others, the following problems (let's assume here that T is a general topic with subtopics T1 and T2):
Fewer answers: I ask about T. Someone gives an answer related to T1. The question is re-tagged with T1. Others will assume that I wanted to know about T1 and not about T2, and they will not post their answers related to T2.
Unnecessary friction: I ask about T. Someone gives an answer related to T1. The question is re-tagged with T1. Someone else gives an answer related to T2, but it gets downvoted, as it looks like it is off-topic now.
Accelerated misunderstandings: I ask about T2. Someone misunderstands the question and thinks I wanted to know about T1, and writes an off-topic answer related to T1. The question is then tagged with T1. Now others see the tag and write more and more off-topic answers related to T1, and all of them get upvoted as they seem to be on-topic.
Moreover, editing questions based on answers in general makes the site more difficult to follow. The users assume that this is a Q&A site: there are questions, and there are answers to them, and these two things are well-separated.
Ideally, each post should be readable in a linear manner: you first read a question and it should make sense; then you read answers and they should make sense. If you tweak the question based on the answers, you can easily confuse the reader ("why is this guy asking the question if he already seems to know the answer?"). For instance, consider this:
- I ask if there is a subtopic of T which has this-and-that property. Someone answers that T1 satisfies the properties. The question is re-tagged with T1. Now the question no longer makes any sense: why would I post such a question if I already knew about T1, which clearly answers the question.
In general, I just have an uneasy feeling whenever people edit posts based on answers. This is a bit similar to, for example, editing the title of the question so that it summarises the answers. It might look like it is helpful, but actually it just makes the site more difficult to follow.
In summary, to me it is obvious that re-tagging based on answers shouldn't be done – so much that I fail to actually see why someone would like to do this. Would it just be a kludge that overcomes the limitation that we cannot have tags in answers?