… once you have a chief executive chosen by popular election, you are in trouble. The “extreme” measure of the legislature removing the head of state happens much more readily in parliamentary systems … we are just about the only country without a parliamentary system that isn’t pretty far along on the autocracy spectrum.
… the problem with popular election of Prime Ministers, and especially of Presidents, is that they become much more powerful than legislatures. They have national legitimacy, they can present a unified front, and they can dominate the news media. Separation of powers is a pipedream.