[PeterisP]

"why not let them stay?" has a simple answer that not letting them stay has some benefit to some USA citizens in reducing competition in the workforce. One may argue whether benefits of this 'labor market protectionism' really outweigh the drawbacks in economic competitiveness, but after recent elections this choice has been made and "jobs for Americans instead of immigrants" has become an explicit goal.

It really doesn't make much practical sense to attract students, educate them, and have them leave. But having the flow of student immigrants be naturally regulated by the admissions process, as you propose, seems to be putting the cart before the horse policy wise. From the gov't perspective, the interests and education goals of the (potential) immigrants are irrelevant but the flow of skilled immigrant labor matters a lot - what would be a practical solution is to make a decision about what amount and kind of post-college immigrants staying would be best for the interests of current USA citizens (which might reasonably be close to 0 in some areas of study), and then set the limits and conditions for student visas/admissions to match that goal.