Many problem in problemset have tags that don't have anything to do with the problem, this is rather annoying, especially if you are trying to find problems for a specific topic. As far as I know anyone who solve a problem can edit the tag, which basicly means that anyone can copy someone submission, and edit the tags. For the problem 1713D - Отсчет турнира form the most recent div2 round induk_v_tsiane has been repeatedly deleting tag 2-sat, and someone adding it back.
Also it seems that solution for this issue is not that hard to implement: either a minimum rating to be able to edit the tag, or leave it just for problemsetters.
There is AFAIK a minimum rating for tag editing, namely 1900 rating (candidate master).
In my opinion, leaving them to problemsetters only might not be a good idea, as tags can also reflect another approach to solving the problem; for example, if I found an alternative solution that uses graphs instead of data structures, putting a "graphs" tag is valid in my opinion.
For the issue of "someone adding the tag back", is your issue similar to that described in this blog post? Perhaps it is the problemsetter who added the tag, by accident or because they could link the problem to 2-SAT. In either case, in my humble opinion more care should always be given to removing tags than adding them, and unless the tag is very clearly irrelevant, I won't recommend removing a tag.
Thanks for the clarification on a minimum rating.
As for tags that can be somewhat liked to the problem, I personally would prefer not having them, since main usage of the tags, at least for me, is to search for a problem on a specific topic.