So colleges – at least the majority of higher ed institutions that are not swamped with amazing applicants like some elite schools are – take a lot of international students for largely economic reasons. What's the big deal? Why shouldn't they take them? Diversity is good!
The problem (and note, crucially, that it's not a problem for the entire university community) is that these students can be poorly prepared to succeed in a US classroom and very little is done to help integrate these students into campuses often located in rural areas that lack much diversity. Let's unpack that a bit, and note that not all international students and not all colleges are identical on this point. Obviously.
First, international students often have an educational background that amounts to intense math, science, and computer skill training with nothing resembling what we broadly recognize as a Liberal Arts type education here in the US. This means universities will do one of two things: either put international students in courses where some will struggle mightily, or alter their curriculum so Tech-oriented students don't have to take any liberal arts or humanities courses. Those are both bad outcomes.
Another big problem is basic facility with English, which I hope we can agree is a prerequisite to any student succeeding in a US college classroom. I don't care if immigrants to the US speak English or not, as history shows that over time they and future generations will learn it inevitably. But for a person coming to the US specifically for the purpose of taking college courses, not being able to speak, read, and understand English is going to be a big problem.
I hope that isn't parsed or misconstrued to endorse some sort of racist closed-door policy. The issue is that – OK let's be real, we're talking specifically about China here – international student applicants are certified to have English language ability in a process that is clearly flawed. I'm not saying Chinese state policy is to cheat standardized testing and fudge applicant backgrounds and qualifications, but…it totally is. This is common knowledge, not a conspiracy theory. Administering standardized tests in China is a nightmare issue for organizations like ETS or College Board, and applications from China regularly have certification of skills and degrees completed that are of doubtful provenance. This is not the students' fault in the slightest. This is a situation beyond their control.
Anyway, the 80s movie stereotype of the Exchange Student who no-speak English is generally false, but in recent years with the sharp rise in recruitment from China there are in fact some issues.
The second big issue is support and integration. You cannot accept a couple hundred Bengali or Ukranian or Chinese or Turkish students and just drop them in the middle of rural western Michigan and say "OK, good luck!" Support resources for foreign students might not be urgently needed in Chicago or San Francisco or Miami, but they definitely are in Rural Rust Belt, Missouri. Real efforts to integrate students with the larger campus are rarely attempted. Instead, schools more commonly take the "self contained biosphere" approach, setting up a separate living environment for all international students and just sort of telling them to make the best of it. I've never been an international student, but it's not hard to imagine how social, personal, and psychological issues could be a big problem. I imagine myself dumped not into Beijing but into some rural city in China where I might be one of only 100 English-speaking white people and I do not have a hard time seeing how that could be intimidating and alienating.
Let's be honest again and recognize that in some parts of the US, the non-campus community might also be hostile to the idea of universities (especially if public) catering to thousands of people speaking foreign languages. I don't need to elaborate here; suffice it to say that is a problem and it is rarely dealt with in a systematic and serious way.
International students are great. Don't get me wrong. It is ironic to me that every non-US citizen student who has ever taken my (often required) Intro to American Government course has passed it, often with an A or B. These are good students as a group; smart people and a pleasure to deal with. Unfortunately they are often (though obviously not always) put in situations where they are going to have a hard time succeeding through no fault of their own. Their government is telling them "Go, do this or you have no future" and on the American end we are saying "Yes, come, show us the money!" and it doesn't take an overwhelming amount of cynicism to see how that doesn't create the best set of incentives.
I don't see a likely solution so long as the vast majority of higher education institutions in the US compete for a stagnant or (in some states) shrinking population of college-aged people. Tuition will go up, but so will the discounts given in what is a very competitive environment for highly qualified students. Someone and something has to take up the slack.