Harvard professors Levitsky & Ziblatt assert: “Politics without guardrails killed Chilean democracy.” They then describe Salvador Allende as participating in an erosion of democratic norms, but somehow, they leave out the well-documented American support for the overthrow of this popularly elected figure. They create the impression that the “military seized power” because the political parties had destroyed democratic institutions. Henry Kissinger, former Harvard professor, had a lot to do with this outcome. See pp 115-17 of “How Democracies Die.”
The more general point is that military interventions, secret or otherwise, are self-evidently lethal for democracies. The military is of course not a democratic institution, and should never be involved in domestic politics. It should not be a prop, or a political football.
Another reason to have a national vote always elect the president is that the military composes an appropriate share of the national vote, whereas it may constitute an unnaturally large fraction of the vote in certain states, thus exercising disproportional influence on representation in the Electoral College.