How does this compare to the fraction of foreign students studying in other countries and choosing to remain there?
Generally speaking, American exceptionalism is nonsense. The US isn't the only free country, the freest country, the only democratic country, the most democratic country, the richest country, the most diverse country, a city on the hill, divinely inspired, uniquely blessed by God, the only capitalist country, any of that nonsense. It was some of those when Tocqueville wrote Democracy in America, but it hasn't been for decades. But the US's research university system is unique in the world, and nobody else even comes close.