This would make elections much, much fairer. I can sum it up in a couple points.
-Whoever gets the most votes, wins. (Does this not make sense to anyone? Is it fair that someone who got less votes than an opponent should win?)
-Every vote will have an impact in the election, not just the swing states. (cough, Ohio, cough.)
-It will almost entirely eliminate the practice of "pork barreling" e.g. giving undue attention to swing states in order to better your political party's standing.
-Every person's vote weighs the same, so Californians don't have to have barely a quarter of the voting power of a person from Wyoming.
When most people's votes don't matter at all (just look at all the states where the political parties didn't spend any money), you no longer live in a democracy, where every person's voice should count.
If you think a proportionally representational system doesn't work, all you have to do is look at, say, Sweden. Why would people want to stick with an Industrial revolution aged voting system like the Electoral College?
How would you proportionally elect someone to the Presidency? Perhaps each candidate holds it for a certain number of months, based on the proportion of the vote?