I'm not sure about your last point, given that Trump lost the popular vote.
Trump would never even have been a candidate if the president were chosen by independent electors. The electoral college we have now is sort of the worst of both worlds--electors who are expected to rubber-stamp popular opinion, but who are not allocated in proportion to population.
The major difficultly with the idea of independent electors is: who chooses them? The original idea was that the people would vote for electors who reflected their political philosophies, and the electors would then make their own, independent judgments about which presidential candidates were best. But predictably (in hindsight), this promptly degenerated into a de facto popular election when the would-be electors began to openly declare their presidential preferences ahead of time. You might consider solving this by electing the electors before the presidential candidates are even announced, but another thing the founders didn't anticipate was the rise of political parties (again, obvious in hindsight). Party affiliation means electing the electors first would turn every presidential election into "generic democrat vs. generic republican," which would leave the parties free to nominate hyper-partisan candidates. The current system does at least encourage, if not guarantee, nominal centrism.
Unfortunately, there isn't a simple solution, and even the best system is going to fail sometimes. But the modern world operates so close to the edge, and the consequences of failure have become so severe, that we really can't afford to slip up anymore.