It's not needed if spell names are specific enough, but does it hurt?
I think for something like wish it is actually useful, as that is a common English language word that can show up in a lot of posts and makes it harder to find those posts related to the wish spell.
For something with a specific name like "glyph of warding" you can probably rely on the search function and is:question to find those posts that are related to the spell. Same goes for "simulacrum".
The advantage of non-tagging is also that tagging needs to be maintained, and new posters very likely miss rarely used tags. So this taxonomy will never be comprehensive.
I don't know if a policy here needs to be very simple, or if it is OK to have some nuance. If it needs to be super simple, than probably all spell-name tags would have to go, including the useful ones.
On the other hand, does it hurt to have those tags? As long as someone is willing to add them, I do not see them being a problem either.
As per request I see these problems pointed out by other posts here
They take up common English word space: I think that is a feature, not a bug. It helps me to find posts about the wish spell, rather than posts where someone wishes to do something.
They take up tag slots: In updating 40 posts this morning, there was exactly one that had all five slots filled. That seems not to be any issue in practice. (Some of the people here with the requsite mining skills can probalby provide a quantitative answer on what share of posts has all 5 tags).
They reinforce popular systems by having them squat on tags for things like invisibility, which could be applicable to super hero powers and such, not just D&D spells. This has a bit of substance. But this would not be any issue with tags for spell names that are clearly from D&D pedigree like "tiny hut" or "glyph of warding". Those will not be squatting on anybodies turf.
I in general feel it is easy to be tempted to establish rules and regulations in a well-meaning attempt to improve things.
This is a community maintained site. There may be wisdom in letting the community maintain things as they like, instead of regaling them with well-meaning rules. In my experience, that can easily feel exclusive, and while I understand the need for some rules, I would suggest to keep it to those areas that really cause problems.
(That I updated like a bazillion posts this morning - well, 40 - has more to do with my stupidiy about how to do it than it being an issue of spell tags, that could have happened with any kind of tag).