I thought Dubya became President precisely because he was a Bush?
But you are right, we did choose our monarchy/ monarch, and have done so for quite some time. We decided that having an all-powerful religious nutjob in charge was a bad idea and restored a monarchy with reduced power after the civil war. We got rid of the Stuarts and replaced them with the Oranges in the Glorious Revolution. Hell, even Harold II was chosen in 1066. Admittedly 'chosen' in these contexts means by a small wealthy elite, but I see little difference between that and the 'selection' of candidates for the US Presidency. And by tacit consent, if we didn't like our current HoS system there would be a popular republican movement. There is no desire for that. We like our system because no one in government has too much power and they are all easy to get rid of, except the monarch who has no real power to worry about.