FWIW the founders never intended for the citizens to have a direct vote for either the President or the Senate. They wanted those offices free from the political pressure of the masses in order to assure that we never had the kind of government that we now have, i.e., a Robin-Hood style democratic electorate that could vote themselves money from the treasury.
You are exactly right about that, and we have bastardized the electoral college which was designed to pick a president and not be a superfluous extension of a popular vote.
In that sense, we are NOT a republic. And it’s been for the worse.