I don't think we need to go banning anything, but I do see the "unknowingly unsolvable" issue as a challenge. However, I think the solution is as simple as making better use of the tags we already have. There are tags for many common "niche" subject areas, such as video-games, movies, language, geography, etc. And failing that, trivia is a pretty good catch-all, for any puzzle that requires "nonessential, specifically detailed knowledge on topics of popular culture".
The issue is simply that often people don't always apply the appropriate tags. This is possibly due to the misconception that a puzzle, or its solution, needs to be about something in order for it to be tagged as such.
For example, a good riddle would not usually require specialised knowledge and its solution would be an everyday object/concept, so tagging riddle would be sufficient. However, if the solution, the presentation, or any of the clues, required more niche knowledge, it should probably have additional tags to indicate as much.
Appropriate tagging should not only categorise and curate, but it should also set the expectations of the solvers.