If we had a direct, popular election, cheating in one or two states that were already heavily partisan (with, say, Democratic governors and attornies general) could affect the election as a whole.
If there was another close election (like Kennedy/Nixon), and one candidate wanted a recount, he could demand it from every single precinct in the country--because picking up an exttra vote, anywhere, would benefit him.
In Pennsylvania, there's evidence of massive cheating in Philadelphia, which tipped the state as a whole into the Dem column. Good luck prosecuting Philly fraud with a Dem governor