And yet, constitutionally, we do not vote for our president as a single people. That is a broadly-held but mistaken belief. It's also a broadly-held but mistaken belief that we live in a thorough democracy: we do not. Only at the local and state level (and I can't really vouch for more than about one state), is it a democracy. You want democracy with all its warts? Move to Greece: they have actual, true democracy and take it seriously with 70-80% turnout. (Although technically mandtory, the requirement is only enforced by socially held beliefs which the Greeks take very seriously, unlike the comparatively apathetic American voters.)
It's also a broadly-held but mistaken belief that each vote counts equally in US national elections. A single vote in New York counts much less than a single vote in Wyoming (to use extreme examples). This is an important part of the functioning of our nation of states. As long as we have a nation of states, rather than a direct democracy without the structure of individual state governments, the power of the states must be supported against Federal encroachment through mechanisms like the Electoral College.
That it is possible to elect a national leader with what some might consider an appallingly small fraction of the popular vote serves to reinforce states rights. You want your vote to count more? Move to a low-population state. Or to a solidly red or blue state, and vote against the majority. That the Electoral College can override the popular vote has been known for a very long time, and has in fact, already happened. Twice. Those that think it is only a recent problem have not studied their American history.