It wasn't just the U.S. receiving that talent. Latin America, particularly Mexico, Brazil, Argentina, and Chile also saw 10s of millions of European immigrants.[1] Germans, Italians, Jews, Poles, etc, as well as Japanese and Chinese. Canada and Australia also saw significant migration.

So the mere fact of the emigration of European talent doesn't quite answer the question. The role of European conflict driving emigration isn't at question here. But what distinguished U.S. schools? Why were they better able to leverage this accidental human bounty than other systems? It's not like there was a complete dearth of higher education institutions in Latin America. In the first few decades of the 20th century Argentina and Chile were some of the most well-developed nations on earth, scientifically and politically.

[1] Circa 2003 I met a 90-ish-something Mexican born, ethnic Irish docent in the Bisbee, AZ museum. His parents fled Ireland to Mexico and worked a farm in Sonora, then killed in conflict between the Mexican Army and, IIRC, Apaches. He and his older brother trekked through the desert for several days to cross (illegally, I might add) to the U.S. I always thought that was a fascinating story--a nexus of different historical threads that, as an American, you would never really consider together.