Here's a specific example: I wrote an answer to this question: How to professionally handle sexist remarks by a student?
The OP only included one tag. I can think of at least one more tag but I'm hesitating to add it. Since I contributed an answer, maybe it might look as though I have a conflict of interest?
Askers are notoriously bad at tagging their questions, choosing a useful title, and so on. If you answer a question, you are probably best qualified to edit it – not only because you apparently feel qualified to answer on the topic but also because you looked more at the question than any other user.
While you technically have a conflict of interest regarding tag-related badges, you have to perform a lot of biased tag edits to actually see an effect and all you get at the end is a stinking badge. Moreover as tag edits bump the question, they draw attention and can be supervised by other users. In general, once you gain a privilege on a Stack Exchange site, you are trusted to handle it responsibly. Almost every privilege can theoretically be abused.
You also technically have a conflict of interest by bumping the question or increasing its visibility (through added tags). However, as long as you perform the edit temporally close to answering it, the bump does not really change something as the question is on the front page anyway. Even tag-only edits to old questions are fine unless you do some systematic or binge tag editing (in which case, you should announce and ratify your plans on Meta first). As for increasing the question’s general visibility, this is a generally encouraged thing, as long as it does not lead to questions bugging people where they shouldn’t. Again, you are trusted to handle your privileges responsibly.
Finally note that the Explainer, Refiner, and Illuminator badges explicitly encourage editing questions that you answer.
Adding an answer makes the question jump to the top of the front page. That means this is a great time to edit the question to add tags or fix any formatting issues.
Tags are really important for future users to find questions, so if in doubt add an existing tag. If the tag you want to add does not exist, it is worth asking on meta or chat about it.
IMHO, this is totally fine. I've noticed many posts where answering users edit the tags of the question in various Stack Exchange sites. I find many of them useful too.
As long as the additional tag is relevant to the question, there is nothing else to worry about.
For instance, I skim through the live stream of incoming questions in Stack Overflow looking for Python topics. Many times, I see posts related to Python but don't have the tag. I add the tag and also answer the question. There are many expert users subscribed to this tag too. I've seen occasions where a better answer is posted in the same question afterward. This helps both the OP and the community. I would not rule this out as a probable conflict of interest.
