I have launched international hiring processes for PhD studentship positions at my lab. More than once, I have had good candidates who ended up rejecting an offer and going to the US instead because their universities have more prestige.

Sometimes the convenience of these decisions for them was, let's say, highly questionable (although I really hope I'm wrong and wish them the best of luck!). For example, a person from Iran who went there to first be hit by Trump's travel ban, and then the graduate student hike. Here that person would have had a good salary, enough to live well, and no such worries. And even though my university as a whole is ranked worse that the university they ended up in, my group/lab is better on any metric.

I have also had a candidate from an Asian country who really wanted to come here, but their parents wanted their child to go to a "prestigious US university" so they didn't let them.

I do think that if you ask in Europe, almost no one wants to go to the US. At least that's my experience. But in other areas of the world the inertia of the US's reputation is strong.