Alright I'm trying this again, hopefully I don't close the tab like an idiot.
So, to get this answer, I went through the top 10 used Pokemon and their top 5 used moves, excluding status. So it should be about 50 moves a tier, although it ended up not being 50 moves a tier ever because of status. So yeah, let's get started?
Ubers: Dark (5/42)
OU(1825+): Ground (6/46)
UU: Fire (6/47)
RU: Ice (6/46)
NU: Fighting (5/41)
PU/ZU/Untiered: Normal (6/44) and the runner-up is Fire with (5/44)
This will need updating very soon....And if anyone has a better method, please tell me :)