Um, the issue isn't who won the election. We know that under the rules as currently laid out by the Consitution, Kennedy won the 1960 election. Nobody disputes that. The debate is over what metric should matter in a healthy, functioning democracy. Those (like me) who support abolishing the electoral college believe that when it comes to choosing the one elected official who gets to claim to have a mandate from the people of the nation at large, the actual will of the voters should take precedence over a deeply flawed measure of how "widespread" each candidate's vote is.
I don't oppose the electoral college because I hate Bush and Trump. I oppose the electoral college because it's an incredibly undemocratic system that doesn't count everyone's votes. It also doesn't give more power to rural areas, nor does it prevent populist demagogues from taking over. It's just a flawed system that usually matches the popular vote, but occasionally doesn't due to random chance.
This. The OP has completely missed the point; clearly Kennedy was the lawful winner of the 1960 election, just as Hayes, Harrison, Bush, and Trump won their respective elections. The argument in favor of a popular vote is not a matter of re-litigating the past, but of establishing a just government that represents all citizens equally. This is why arguments such as "the U.S. is a 'republic,' not a democracy" and "the founders intended [xyz]" are utterly meaningless when it comes to discussions of constitutional reform, because we are not debating what the United States
is, we're debating what the United States
should be.