That's a real strong argument for the Electoral College. If the problem areas can't be isolated from impacting the outcome, there would never be an outcome. Challenges, recounts, situations landing in the courts would NEVER be settled.
You are very CORRECT and that, I believe, is one of the reasons the Founders devised this system. Given that in 1789 the States were in the horse era with communications limited to that speed, each state would find it near impossible to do a complete count and get it to the National Capitol on time, even given the old inaugural date in March. Having the Electoral College short-circuits that problem and allows for a clear vote.
Now, with our trans-continental (and Hawaii plus Alaska) the problem, even with light-speed communications, is compounded! Imagine this election on the popular vote and we can plainly see that it would still be undecided! Add disputed and provisional ballots, and you just add time to the problem. Then from that morass, you, in this kind of close election, have the legion of lawyers and interested parties challenging the 'official' results in the courts, from State to Federal!
Thus, we could end up with year+ election campaigns AND equally long disputatious decision cycles. NO! NEVER! Once again we must THANK the Founders for their GENIUS and foresight! Vox populi, diputatis eternalis! (Latin sounding, not real)