"under the proposed popular vote system candidates would likely focus their campaigns on dense population centers, buying ads in larger media markets, and making promises to the benefit of the states that have those large cities."
Candidates would, reasonably, campaign where there are more voters.
It's not true that a candidate could concentrate in a few large cities and win. Even if a candidate got every single vote in the 100 largest cities, they'd only get 1/6 of the vote.
You may be concerned that they would OVERconcentrate in large population centers -- say, spending 75% of their time in the 10 largest cities. Handily, there's a nice way to empirically test this idea: within a state, where all votes are equal, Presidential campaigns spread out their events in proportion to the population. I found the evidence in this video very compelling:
https://www.youtube.com/watch?v=_gbwv5hf2Ps
"The way it is now, candidates need to visit the smaller states during a campaign, which provides more fairness."
Empirically, they don't visit all the states now. They only visit swing states:
Setting aside speculation about what would happen, I believe the fundamental principle of democracy is that every vote is counted equally. Under a popular vote, that happens by definition. Under the Electoral College, it doesn't -- any candidate would happily trade a California or Oklahoma vote for a Florida or Ohio vote. Some votes are worth more than others, and that's wrong.
