That's the exact and precise opposite of the truth. C'mon, think! With the electoral college, there is no motivation for a candidate to campaign in a state that is sure to go for him or for his opponent. With the EC, 10,000 more GOP votes in NY, or 10,000 more Dem votes in Oklahoma, won't make one whit of difference. With a popular vote, 10,000 votes will matter no matter where they come from. As it is, candidates DO NOT spend time trying to please "big state needs," but rather to win votes in swing states.
Sez who? There's no reason we cannot have a pop vote that requires a majority. And no one is suggesting a parliamentary system.
Yet again, non-issues. We can require a pop vote majority or we can use a ranked voting system. But you are right in that we certainly don't want a leader who won only a minority of votes. Like now.
With a popular vote, candidates won't visit or try to satisfy little states' issues. They'll spend all their time trying to increase the popular vote in big city areas in the big states. So they'll spend all their time in California, Texas, NY, FLorida, etc. The other issue is if you're doing away with the electoral system because of some perceive unfairness, than you have to eliminate the Senate. Why should little states with a few people have two senators when huge California only has two senators? The Senate is just as unfair.
If you pass a constitutional amendment requiring a majority of the popular vote, there will be many occasions where you won't get it. Any time there are third party candidates, there's a big chance no one will get a majority of the popular vote. That happened in 2016 when Hillary got 48%, Trump 46% and others 6%. However, the electoral vote system eliminated third party votes. So the electoral vote always gives one person a majority. The only reason a Parliamentary system works is because the smaller parties make deals with the larger ones. You can't do that in a popular vote system when you're only counting votes. There are no negotiations after the fact.
Trump did not win with a minority of votes. You just refuse to accept the Constitution. He won with 57% of the electoral votes. That's what counts. Popular vote doesn't mean anything.