I wasn't using the term as a put down - if you are going to have a head of state with real power, it is better for them to be elected than get that job some other way.

The term, "hereditary monarchy", which is often used, implies that it is possible to have monarchies which are not hereditary. Using the term to refer to the American system seems fair enough - and I think it it useful to recognize that the powers of American presidents are comparable to those of European monarchs at the time of the Founding Fathers. As Little Hawk said, not absolute powers, but very substantial.

The special feature of the American system has been that the head of state is elected by popular vote (or rather by a body of electors elected by popular vote), with a time limited period in power. And it's not meant to be hereditary within ruling families either, though it has seemed to be drifting that way at times.