Lots of great universities in China for them to go to.
Lots of American born Asians. You know, second generation, third generation. Probably don't speak Chinese.
Really.
No there aren't. And I fully support giving out visa by the hundreds of thousands to foreign students who are qualified and willing to pay the exorbitant out-of-state tuition fees. You know, the folks who are following immigration rules, spending money here, want to succeed through hard work and talent, and who have the ability to make the world a better place (many stay here, and many go back home to improve their home countries).
As for the "great universities in China"... not one is ranked in the Top 100 in the world (as ranked by SHANGHAIranking.com), while the US has 52. The top 3 Chinese universities (their Harvard, Yale, and MIT) ranked in the same grouping with Baylor, Case Western, Emory, Tufts, Virginia, etc (#101-150)... certainly some decent US campuses, but not exactly global powerhouse universities.