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.