Other countries manage it without their leaders turning into kings.
Other countries aren't formally Right-of-center undergoing an attempted takeover by its internal Left. The U.S. has checks and balances and intentional slowdowns built into its political processes, so it would take a near-king to overcome in a timely fashion those holdovers from our prior traditional past.
People should be free to vote for whomever they want.
Not to an extreme. People should be free to swing their fists, too, but there are limits to that. I think you should get to elect whatever bastard you want, you just shouldn't get to elect the same bastard in perpetuity.
But I do feel some discomfort in holding this position, because like regulating money in elections (which I'm against), it is infringing on political speech.
Beyond this, your "just think of the restraint that would come from endless power" doesn't exactly sway me.
He brought about the "New Deal" to help the nation survive the Great Depression,
FDR was a communist and enemy of America. Just like the current office holder. The problem is, I figure about a third of this country is the same, so occasionally we're going to get people in the White House who have absolutely no business representing the country. As long as America has a significant population of Americans who hate what America stands for, all the more reason for term limits, to limit our mistakes.