Even if some of my examples are flowed, the point remains the same. Many pokemons are hurt very badly with the ability Contrary, and can fall one or even 2 tiers with this ability(no QD Volcarona anyone?) .
Also Lucario with Close Combast is still shit, because Lucario's defenses are shitty, and without the Atk boosts, Lucario won't be doing anything...
Something else that you seem to be missing too:
Contrary doesn't make unusable pokemon viable often, no matter how you look at it. ~10 Pokes that become usable after being unusable is rare not often.
Also you are completely ignoring the fact that Contrary has one characteristic of tier F:
So Contrary doesn't belong to tier S no matter how you look at it. Not only it doesn't fill the requirements that an ability must to be in that tier, but it also has one characteristic that only tier F abilities have. So, imo, Contary should go in Tier A, AT BEST(Contrary sucks on much more pokes, than to the pokes that it makes usable from unusable)...
Finally your example about not using the ability on a set-up mon is completely irrelevant. We are seeing these abilities theoretically, and in a vacuum, so your example does not hold any ground. So if a set-up poke theoretically got Contrary, you couldn't come and say ''don't use Contrary on it'', because it would be his only ability, since again we are talking theoretically and seeing the abilities in a vacuum.