Evasion Clause was banned because it was broken:
Chansey used Minimize!
And that's pretty much good game unless you carry something that can OHKO Chansey, Aura Sphere, phazing, or you get really lucky with a critical hit or with status, the same, but at lessen degree can be said of any minimize user, and the best part is even if you phaze her, she can just comeback once the phazer was defeated and repeat the same with total impunity. On ubers it was unbanned because it was tested and the results said it was not really broken at all on ubers, as Kyogre's omnipresense and perfect accuracy Thunder, Aura Sphere, Ho-oh's/Lugia's phazing, and the general higher power of normal Pokémon on the tier and the really low power of the evasion users made it really unreliable, but in OU that's other history. The clause was carried more for legacy and for fear of previous monster with that, anyway, as Chansey/Shuckle on RBY and GSC were literally impossible to handle with Evasion Clause off, you can phaze them, yes, but nothing will stop them from come back, and repeat the same until you run out from PP's before them, your unique real option were Explode things and pray for the explosions hits.
OHKO's moves were banned because they were proveed broken, Articuno + Lock-On style moves = InstaK.O's per two turns to anything, and by other hand, you can't break a wall? Fissure was used! OHKO landed! End. People is already risking with Focus Blast, OHKO moves just have somewhat less of the half of accuracy, and those moves make stall, semi-stall, balanced, and offensive-balanced literaly impossible. That's far more powerful than anything else on OU, and with a really decent chance to land once you used it some turns.
Sand Veil was banned because Garchomp, people prefered to regain Garchomp in exchange to lost an ability, that's pretty much all, Snow Cloack was inserted on the ban just for... flavor wise, mostly. Literally the same did happen with the previous evasion bans like with Brightpowder, but people was also somewhat worried of other abussers, but not too much as of Garchomp. Genesect was voted for being broken, at least that's what the majority said, and if the majority doesn't think that, then it should be unbanned. Moddy was banned for mostly the same reason that Blaziken was banned, but with the OHKO and evasion clauses flavor incluided.
Doubles are other story.
Things should be banned from OU because they are broken, not really for other reason, as the idea is try to archive the lessen number of bans possible for the OU play.