It's just strange to me that they went so far to try to not make the presidency be like a monarch position, and yet term limits were never set- allowing a hypothetical lifelong leader. Why weren't term limits mentioned/included in the Constitution, then? Sorry if this has been previously answered.
The founders' concerns had more to do with absolute power than with the time served. Remember that they also established a judiciary with life-long appointments (and note that this is the entire federal court system, not just the US Supreme Court).
It mattered more that the President was answerable to the public--if he governed poorly, he would be voted out. But if he governed well, there was no reason not to continue re-electing him. On the contrary, he would have all the more experience from his four years in office, and if he wasn't eligible for re-election, he wouldn't really be answerable to the public. (This is discussed in Federalist Papers 69-74, most notably 72.)