In Federalist 68, Hamilton gave some reasoning as to why the Electoral College exists. Now, I think the Federalist papers should be treated with some care. They're often post-facto attempts at justifying committee decisions when that committee had been sitting in meetings all day and just signed off on something. That's very likely what happened with the Electoral College.

That said, the explicit reasoning in Fed68 was to stop someone like Trump:

The process of election affords a moral certainty, that the office of President will never fall to the lot of any man who is not in an eminent degree endowed with the requisite qualifications. Talents for low intrigue, and the little arts of popularity, may alone suffice to elevate a man to the first honors in a single State; but it will require other talents, and a different kind of merit, to establish him in the esteem and confidence of the whole Union, or of so considerable a portion of it as would be necessary to make him a successful candidate for the distinguished office of President of the United States. It will not be too strong to say, that there will be a constant probability of seeing the station filled by characters pre-eminent for ability and virtue. And this will be thought no inconsiderable recommendation of the Constitution, by those who are able to estimate the share which the executive in every government must necessarily have in its good or ill administration. Though we cannot acquiesce in the political heresy of the poet who says: "For forms of government let fools contest That which is best administered is best,'' yet we may safely pronounce, that the true test of a good government is its aptitude and tendency to produce a good administration.

Additionally, it's also justifying decisions in light of pro-royalist critics (both foreign and domestic) who said democracy was a trap and the rabble can't be trusted to decide on their leaders. As a result, the Constitution doesn't go all in on democracy, and you have this stuff above about one of these not-quite-democratic mechanisms are meant to prevent a populist dullard from gaining the office.

Those royalist critics are all but extinct now, but we're stuck with some of the things designed to counter their objections.

Since then, the US has put in several measures undoing some of the not-quite-democratic stuff. For example, universal suffrage, President and Vice President elected as a pair, senators elected by the popular vote of their state, and the parties having primaries instead of appointing candidates. It's been an improvement for the common people at every step of the way. Fledgling democracies looking for how to structure their government have largely not chosen to repeat the mistakes of the US; not even one's the US itself helped setup, like Germany, Japan, and Iraq. They've preferred European-style parliamentary systems.

So we've got this Electoral College thing that, at best, is there to counter arguments nobody makes any more, and at worst, was rubber stamped by a committee that wanted to go home for the day. It's shit, and it needs to go.