If The Mombasa MF had been a PM rather than a POTUS, he would have been out on his keester before the end of his first term. The parliamentary system also has many features that make it unattractive (or unworkable) here, for example, proportional representation. One of them for example: if the Gay Global Warming PETA Commie Party got 2% of the national vote, they might get a seat or two in a parliament.
Our founders voted for a stable, four-year executive (The Confederates, six), never dreaming that Presidents would become tyrants, or that the sovereign states would be so reduced in power as to have '0' to say in the Federal Government.
What they really never foresaw was the rise of a media---which really didn't exist in its modern form in 1787---that would be able to cow and intimidate ALL those checks and balances branches into submission. The powers still exist. We just have no one who will use any of them.
You are right, though, that the horrible weakness of proportional representation is that it allows fruitcake parties like the Greens or Nazis to obtain real power through . . . intimidation and threatening government shutdowns if they don't get their way.