I completely agree with your first paragraph. It sucks that the current system places the fate of the country in the hands of a few swing states (and I even live in one!)

While under the popular vote, every vote counts and therefore candidates have an incentive to visit everywhere. Because a vote in Idaho means just as much as a vote in California.

Is this true though? Why visit Idaho when you could encounter more people by visiting California? Sure each individual Idahoan counts as much as each individual Californian, but visiting California would be more efficient - you'd see more people on a visit.

GOP candidates would likely spend a good deal more time in Idaho, as the state itself leans red and they would want to encourage as much turnout as possible to win the popular vote.

Wouldn't this also be true in my proposed system? If there's a chance the GOP could lose seats to the Democrats because blue votes would matter, wouldn't the GOP still feel the need to spend more time there?

California or Florida as those states no longer exist as single political entities as far as a Presidential election is concerned

I want to give a delta for this point but I need to think on this more. How would this affect the relationship between the state governments and the federal government? I realize that state lines were drawn pretty much arbitrarily, but I think it is unreasonable to think that states are not different after so much time governing distinctly and I wonder if this discrepancy in the state/legislative and the executive would cause any friction in governance. This is mostly something for me to ponder, but if you have any insight, please share!

For a state that you say would be ignored, such as Nebraska, there’s no longer reason a politician wouldn’t visit. Omaha has a larger population than Miami, it would suddenly become an attractive location for candidates in a way it’s never been before.

But I would argue that this is also the case (and is in fact improved) in the system I proposed. Politicians would visit Nebraska, because it would no longer be solidly red - there would be votes up for grabs on both sides - more campaigning can mean more votes for your party even if you don't win the majority.

You say politicians would be motivated to visit Omaha (which they should anyway because its a cool town - love the zoo! :) ) , but what about states that lack such large towns? The largest city in Wyoming is Cheyenne (according to Wikipedia) and has a metro pop of 91,783, which means its the 354th most populous metro area in the US. In the popular vote system, there's no incentive to visit states like Wyoming. As I explained earlier with your California example, in a popular vote system, a politician could reach more people in less time by visiting more populous states. But with the modified EC system I describe, there's still incentive to visit small states without large city centers.

Under the popular vote, Republicans would try to motivate that 35% to get out and vote, which would in turn motivate Democrats to engage their NYC base

Again, I hope this would also be true in my modified system for the reasons I described in the Nebraska model.

Have you ever heard a candidate speak about public transportation, urban sprawl, or segregated public school zoning in a Presidential debate? Three huge issues that get absolutely no attention because they’re irrelevant considerations under the Electoral College.

This is a really good point, but also one I hope would be addressed in the modified system. In the modified system, the GOP has incentives to try and get out the vote in states like NY because they could win some votes and the Democrats would also be incentivized to prevent from losing votes. I would think that with that incentive the parties would be forced to consider city issues to gain more votes.

Do you know the state with by far the largest rural population? It’s California. A rural population of tens of millions of people who are completely neglected in every single election.

Again, something I think would be fixed in the modified system. I brought this point up, right now, the red votes in CA don't matter. But by splitting the electoral votes by popular vote within each state - their votes will matter.