With that, the US is widely recognized to have the best universities in the world. A lot of countries claim to take education seriously, but the result is often very mediocre.
Very few people will pick IIT or Beijing University if they are offered spot at Harvard.
People go to Harvard not for the excellence of the education, which I'm sure is good but is pretty much equivalent to top state public schools, but for the network and the signaling.
Network - one of the best things you can do is put a bunch of intelligent, highly motivated people in one room and have them work on stuff together. Top tier universities are basically this. The actual education offered on top isn't that relevant as long as it's passable - these people will find a way to educate themselves
Signaling - having Hardvard on your resume is a global signal of your status and opens up so many more doors by simply having it listed by your name
There are plenty of academic opportunities at Harvard that are not available at state schools. Because they attract many of the top students in the world, they're able to offer highly accelerated or advanced courses that other schools can't.
Very few people will pick IIT or Beijing University if they are offered spot at Harvard.