Monument can make Possession turns worse, there's not much more to say about it in the general case. If their deck is pure Monument playing, well it's not a great Possession target, but still not impossible to have situations where you can get more benefit out of it than them. If their deck is more of a mix and you only need to play 1-2 of their Monuments to get something nice with their deck it could still easily be worth it.
I'd say Bishop and Goons are even harder to get good usage out of when Possessing.