Would this be tier 0?

[SinsI]

And that matters even less. Is Pazuzu more likely to work for paladins yes or no? That's the only relevant part of the discussion.

I'd say Binder or Warlock has a much better chance of getting any demon to grant him a Wish. And a commoner can stumble upon a self-resetting Wish trap. Neither of those are relevant to tier discussion - external entities and items are not class abilities.