Indeed, though if you make that route too easy (or with limited oversight), you end up with diploma mills that aren't actually educating anyone. Incentives are hard to align well.

It wouldn't be hard to select and accredit at least the better universities. Giving an automatic work visa to every foreign Ivy graduate should be a no-brainier. You could take the top 30% or 50% ranked US News universities and accredit those, or some similar heuristics.

Great point, and since the post-graduation right to work is already a thing I believe this has already happened