Mihawk is the Shichibukai who come the least in meetings according to Doflamingo(the least expected) and when he became bored of the war, he left. Clearly he doesn't care about the governement and do what he wants. Won't be surprised if it was the governement who pledged him to become a shichibukai, not the way around and probably Mihawk accepted just because he didn't want to be assaulted by admirals in daily basis. Having a yonkou level fighter up in the air like this is surely a threat to them especially if they judged they didn't have strong enough resssources to handle him. Better make him a friend of us