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?
Not to mention it reduces the hidden incentive to suppress the vote by greatly reducing the relative power of said tactic. By placing the electoral vote above the popular vote there is no drawback to winning a state's electoral votes with a turn-out of 30% vs 50% vs 70% where as if there's a national popular vote, it's the raw winning margin of total votes that decides the election so winning Texas 57%-41% with the state having a voting-eligible population turn-out of 54% won't be as good/important as winning Texas 57%-41% with turn-out of 70%+.
Consider that in 2012 Democrats had a winning vote margin of 3m in California, ~2m in New York, and ~880k in Illinois while Republicans had a winning vote margin of 1.26m in Texas, ~500k in Tennessee, and ~490k in Utah. Of course I recognize that there's population differences but the point is that with the national popular vote, you have to win the votes of people as opposed to the "votes of states" and that means votes in one state are worth as much as votes in any other state irrespective of said states' population.
That's different than how it is currently with the Electoral College because the relative "worth" of a state's population is automatically tied to its electoral votes, regardless of how many people actually turn-out. So Texas is worth 7% in an election (38/538 EC votes) regardless of how many people vote. By going to the popular vote you eliminate that disconnect and then have an incentive to expand the electorate with things like automatic/same-day voter registration and early voting because candidates won't be chasing arbitrary geographic-based votes (Electoral votes), they will be trying to win more universal votes (the popular vote).
In a 50/50-ish state that could easily decide the election because of its relative position, Florida Republicans are far more concerned with maintaining the state's felony disenfranchisement that
blocks 10% of the state's electorate (and 23% of the state's blacks) from the polls than they are of expanding the electorate with increased voting rights.
edit: clearer wording
I presume that you are also then in favor of going to direct elections for PM of Canada (or Governor General?) based on your avatar.
If not, then wouldn't US electors elected by district, who then select a president based on the majority party, be equivalent to MPs determining who the prime minister should be based on the majority party? Certainly it's possible that the PM's party could have fewer total votes than the runner-up party as long as they win a majority of seats.
It's more likely the US abolishes/nullifies the Electoral College than it is that we adopt a parliamentary system and I doubt people who favor the US adopting the national popular vote would favor switching to a PM appointed by a party elected under first-past-the-post.