A lot of people from all over the world are trying to get into US schools because it's a way to get a US visa, and legal residency in the US is valuable enough that people are willing to go to great lengths in order to obtain it.

This isn't just a hypothetical, a guy I know from Europe who is currently enrolled in a master's degree program in the US told me outright that the primary motivating factor for him to get a master's degree was because it was the most expedient way for him to get a visa to the US. I know other people who have deliberately enrolled or sought to enroll in higher education programs in other countries they wanted to spend time in, as a way of getting a visa, plus in some cases a stipend from the government of that country.

Certainly some people who attempt to immigrate to the US via the educational system are in fact doing valuable research work - but I think the vast majority of them are not, and I don't really trust the current leadership of the NSF to set up systems that accurately discern between research programs that genuinely benefit the country or the world; and research programs that are actually an excuse to get US visas to smart but ultimately mediocre people from other countries who would prefer to be in the US rather than their own country.