Electoral College elects The President. No other type of election works like that.
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It's not the only thing that we should have changed over time. I disagree about Madison being "the guy" who came up with it, he only agreed with it due to the reasons at the time (which again changed, so it should have changed). Madison preferred a popular vote for President as the ideal vote method.
Honestly post Civil War should have called for a massive reconstruction of the country, but was fumbled badly for the easier route of just patching the wounds and hoping things would work themselves out. They never did.
He supported the popular vote, right up until the 3/5 compromise.
He changed his mind during the convention of 1787,
Remember, before this the argument was that congress itself should elect the executive, or state legislatures. Madison (and Hamilton) pushed this as he didn't trust congress, but nor did he trust the people, but also different states had different voter eligibility laws (for instance, slaves, and later, women).