Given there are currently 762 images tagged with wrestling, and pretty much all of them have specific wrestling moves displayed, would there be value in a "wrestling_move" tag? Or would that be redundant with "wrestling"?

(As for specific move names, given how the same move can have a handful of different names depending on the wrestler that uses them, that sounds like more of a headache than it's worth.)

Technically, wrestling is an alias of wrestling_move. Since an image has to display a wrestling move (even if unnamed) to be able to fall under wrestling subject. Otherwise it would be impossible to determine that the type of fighting is wrestling.
As for tagging specific wrestling move names, that would be redundant since it would require too much knowledge.

Yes, it does sound somewhat redundant.
Even basic grapples are wresting moves, no? So it'd apply to just about everything that's tagged as wrestling.

But as for the specific moves, I don't see much harm in tagging those. Not if it's limited to the common moves, at least. So we won't end up with dozens of tags like sitout_reverse_suplex_slam.

I do not think that adding specific tags like that is redundant, but how many people know the names of the moves?
Therefore, I do not think its feasible.
That's a "No" then I guess.