> if there where a direct path from student to staying in the US then people would just game that process
If someone manages to get accepted at a genuine accredited U.S. high-education institution, and completes their studies, and graduates, why not let them stay? I understand there will be a lot more demand to study in the U.S. if such a pathway existed; so you would want to make sure that there are no diploma mills, and that only people graduating from accredited colleges are allowed to stay. Perhaps capping the number of international students at a college to something like 20% would go further in mitigating your concern. The flow of student immigrants would then be naturally regulated by the admissions process, and by the number of available seats for international students in U.S. universities and institutions.
"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.
Most schools are not very good and have very low admissions criteria. These programs operate as cash cows for the university and students come with the intent to find a US employer to hire them. It's why graduate programs in Computer Science are primarily international students, it's not that they're better it's just that the vast majority of them want a job in the US.
If someone manages to get accepted at a genuine accredited U.S. high-education institution, and completes their studies, and graduates, why not let them stay? I understand there will be a lot more demand to study in the U.S. if such a pathway existed; so you would want to make sure that there are no diploma mills, and that only people graduating from accredited colleges are allowed to stay. Perhaps capping the number of international students at a college to something like 20% would go further in mitigating your concern. The flow of student immigrants would then be naturally regulated by the admissions process, and by the number of available seats for international students in U.S. universities and institutions.