...Or be a Major? That wouldn't have been too uncommon in the 1940s, now would it?
That Sisko stayed in power would be mostly attributable to him being a prominent religious figure. Removing him would bring Starfleet's (or perhaps just Picard's?) plans on Bajor to an early ruination. And Sisko would insist on keeping Kira, as he wouldn't be all that thrilled about his religious position and wouldn't really want to interact with his "devout followers", that is, the people wishing to exploit him through the religion angle. He apparently much preferred the more secular forces chiefly represented by Kira.