Re: It's not "why", it's "how"
"While the US system of indirect election is somewhat arcane, it does do what it says on the tin."
correct. it ALSO gives a bit more clout to non-populous states. Many of the compromises ca 1787 regarding the framing of the U.S. Constitution were compromises between people who wanted each state to have equal representation, and who wanted individual people to be equally represented.
The electoral college basically rubber stamps the individual state's election results. It can work both for or against a candidate. but in MANY ways it more equally represents what's going on across the entire nation. So it stays, because it works, and because 'tradition'.
It also forces candidates to campaign OUTSIDE OF MAJOR POPULATION AREAS. That's a GOOD thing. Otherwise, San Francisco, Los Angeles, Detroit, Chicago, and New York City would decide EVERY presidential election. Yeah, don't go there...