No, princess don't need to marry to be queens, (See King's Quest)
The Prime Minister theory is good, but then Bowser would try to kill or kidnap him, I think.
You fools need to play Paper Mario, in which the Minister was shown (he looked like a slightly older, robed Toadsworth in a way) and was captured by Bowser. If you haven't played Paper Mario, there's something wrong with you.
Bowser could have killed the King already, or perhaps he died when Peach was very young, which would explain why Toadsworth tries to take care of Peach. Where Queen Toadstool is, I don't know. Maybe she died too. Maybe Mario is also dead. And Toad, he must be dead too. Yoshi CAN'T still be alive, either. All the Shy Guys are dead. Bowser's dead as well. Luigi got killed by a falling tree covered inm chainsaws, he's dead. Daisy's dead. Wario's dead. Everyone is so dead to me.