There's just one point I have to make: Prankster.
That abuses the priority, allowing immediate setting up without worry of dying before using any moves.
We should all be thankful that Cottonee/Whimsicott can't learn Spore, otherwise it would easily be moved into Uber. Priority 100% sleep? Too busted. Priority 75% sleep? Apparently okay.
Anyway, no, some guys need priority moves, otherwise they're worthless. Scizor may make a niche in UU with Bug Bite, may show up in OU a little, but not as good. Conkeldurr would have to rely on Bulk Up to do much of anything, and a good Psychic type like Alakazam or Reuniclus could easily murder it, since Alakazam goes first, and Reuniclus could wall anything Conkeldurr would use, if properly trained.
Mamoswine would be worse than useless, only having one resistance and 5 common weaknesses (2 resistances and 4 weaknesses if it has Thick Fat), if it weren't for Ice Shard, since, as stated above, Dragons could run rampant.
Arceus would still be uber, of course, but the most popular version wouldn't be as good, since it could spam Judgment instead of Extremespeed, if priority weren't there.