Just a nit, strictly speaking, the electoral college is just a system where states must delegate the power to vote for president to a group of people (the expectation being that they should make an informed decision to further their interests based on facts on the ground in the capital). It's also a form of indirection: you don't vote for president, the best you can do is appoint people you can trust to make a good decision (similarly, there was originally a layer of indirection for senators, who were appointed by state legislatures, not by state vote). Of course, this is essentially abolished because people wanted more direct control over the government.

Regarding district level representation being obviously a bad idea - not necessarily. Since senators represent the state (and wasn't even voted upon directly by the people), representatives are the way local (populist) interests get represented. This only breaks down once when people start having general party allegiance (both at the ballot and in mind share), which I'd argue is itself caused by the fact that we vote directly on appointments which are far beyond our locality (senators but mainly the president), which then spills over to our choices of representatives.