You're assuming that there weren't enough spots for Americans and that they were getting denied due to foreigners. That's not true. For Americans who want a college education and don't get one is mostly because of the cost of education, which foreign students subsidize.
This is a classic case of shooing yourself in the foot only because of a fear of the foreigner.
I thought colleges only had a limited number of slots to accept students each year. Seems like US citizens would be competing with foreign students in that case.
For most colleges the number of available slots is not constrained by some absolute limit but is instead constrained by their income available to pay for all the people and resources needed to educate these students.
Further, the most competitive universities artificially constrain acceptance rates because low acceptance rates make them more desirable.
Imagine we passed a federal law banning the children of parents who make more than $150,000 annually from attending college. Would this just mean that colleges take their same planned slots and give them to lower earning students? No. It'd be massively disruptive and change the available slots.
If you're prepared to pay the same fees as foreign students and get the same grades, they might be happy to have you, but more likely it'll just mean more colleges have to close - foreign students never really took places from domestic students, they subsidised them.
We are going through a similar issue in the UK where a lot of University finances have been setup to rely on being able to attract foreign - mostly Chinese and Middle Eastern - students who pay 2x-4x more than domestic students. Now those students are being pushed away or are turning away, those institutions are questioning their own viability, and are at risk of bankruptcy.
At Ivy League or Oxbridge levels, this might be an acute issue: the running costs are insane, and despite having large endowment pools of cash, those pools aren't deployable to address the problem. Donations to such funds are often earmarked to support certain seats, tenures, scholarships and so on, and can't be used for general spending and teaching costs.
For the poorer schools without endowments (think JuCos), they might not have relied much on foreign student money anyway, so might weather it better. You are just as likely to get to junior college tomorrow as you were yesterday.
A middle schooler's aspirations of MIT, Stanford, Yale, Berkley and so on might now look more likely on paper, but in truth, those colleges might not be there or not able to offer as many courses by the time they're ready to attend.
I wouldn't be totally surprised to see a couple of Ivy League and some lower tier colleges go under in the next 5 years, and for about half the Russell Group in the UK to face a similar fate.
Not sure about the economics of it in the US, but in many countries international students subsidise domestic students, because they pay full fees whereas domestic students generally do not. Back during the financial crisis lowered enrolment of international students was a factor in Irish universities having to discontinue courses, say; they just weren't economically possible without that subsidy.
This is a classic case of shooing yourself in the foot only because of a fear of the foreigner.