Yes, it should be banned
The term “enchantment” has two major, widely-used, mutually-exclusive definitions. Questions about the subject of each definition should definitely not be grouped with questions using the other definition, so using one tag for both definitions is not workable (and there seems to be strong community consensus on this point).
Anything we define enchantment to be, is going to clash with some of our users’ expectations, and that’s going to lead to misuse. This fundamental problem with the term is not going to go away. No matter what future development happens, it seems inconceivable that either definition is going to stop being used (even if D&D dropped its usage of the term, people will continue playing the editions of it where it did, to say nothing of spin-offs from those editions that will also most likely continue to use it). And a third usage appearing in some future product does not make the situation better.
So we should avoid ever having a tag by this name. It will never not be a problem.
No, it should not be synonymized
The problem is that there are two more-or-less-equally valid targets for a synonym: mind-control or magic-items. Picking one seems to sort of “favor” that definition. Synonyms can be helpful here, in that they convert for the user so they can see “oh, this site means this thing when they say that,” but there is no way to present the user with a choice between the two tags.
Even just thinking about it, I find myself going back and forth on which direction I would favor for the synonym, if forced to pick one. That, to me, is a strong indication that there shouldn’t be a synonym.