Good question. The answer is this: a geographical unit, the state, is recognized as the fundamental subdivision of the United States. It is the states--not races, ages, classes, or religions--that are represented in the Senate. It is the states--not races, ages, classes, or religions--that have their own governments.
Any federal system divides people on that trait. The states are, by definition, divisions based on where people live. Shall we abolish them, too?
Yes, the definition of states on the basis of geography is archaic. But it is so entrenched in our politic consciousness to be perhaps irreversible. One could make a good argument for maintaining the electoral college and our current system of federalism because it would be too unsettling to our past experience and national history to be worth the change.
But you seem to want to defend the electoral college in a sort of de novo review...that it would actually be a good system were it put into place only today, because it demands that a candidate receive broad support. I'm arguing this is not true, and many other systems would more truly demand broad support.
The electoral college allows a candidate to completely ignore any minority group as long as the majority is geographically dispersed. I don't think this is a desireable attribute of a modern political system.