So, the ascent of U.S. universities to high status on a worldwide scale, happened in the first half of the 20th century really. Why? Well, because Europe was tearing itself apart in two world wars, and the U.S. sat out the first half of both of those, while receiving a lot of talent fleeing those wars. If you have the money, and the former top-of-the-heap has bombed their wealth into rubble, it doesn't require any ma…
This is a general misconception you hear that America's dominance in the world (and universities) was due to the "old world" imploding in WWII. It obviously helped the US but already in the early second half of the 19th C America was dominating the industrial revolution, by a wide margin, and had cemented it's place as top GDP (overall and per capita), top global talent magnet, and top overall technical education lev…
I don't think that alone would have made the US into the superpower it is today, in particular in terms of science. That was clearly a result of the two world wars that devastated Europe. If you look at the scientific discoveries the US really became the powerhouse after/during WW2.
It's somewhat ironic that the US which was founded on escaping the large "unfair" inequalities of old Europe and a strong anti-establishment/anti-elite basis has since become a beacon of a new elite/establishment and inequality. The "anti elitism" that was always part of the US psyche is now almost completely about intellectual elite (scientific/academic elite) not economic elite.