Think about this: there are a number of elections that have a very small popular vote margin. What if this gets less than, say, 20,000? That's entirely possible. In a strictly popular vote election, what's to stop each side from scrounging up votes or invalidating votes in every county in the country?
The most contentious and litigated election is probably the 2000 election. The electoral college contained those shenanigans to Florida alone (and largely to Miami-Dade and Broward countries, specifically).
There are four main problems with the US election system as I see it:
1. Voting needs to be mandatory. Americans who love "freedom" chafe against this but optional voting undermines democracy. You can see this in the organized efforts to suppress voting and disqualify voters by US political parties.
2. The US needs preferential voting. Third-party votes are otherwise largely a waste.
3. Paper ballots with optical recognition only. No punch cards, certainly no electronic voting. You need the paper trail of actual ballots. This could be filling in a ballot and validating it with a machine or using a machine to print out a ballot. These have an exceptionally low error rate.
4. Stop politicizing the election process. Like, why is the supervisor for elections an elected political position? This is the case in Florida, for example. Likewise, you have the Senate majority holding up election reform because of there is suspicion this will help the Democrats in the House who passed it. Seriously, Mitch McConnell needs to go to jail.
5. I'm fine with states being represented in the US system. The problem is that this system was designed at a time when populations were rural and cities were small. I don't think anyone predicted the disparity between ~40M people in California and ~150k people in Vermont having 2 Senators each.
You'll note that none of these are having the popular vote. IMHO that's fixing the wrong problem.