When I had a friend deported for losing the lottery (she had a masters in a math related field) our friend group had a lot of discussions about the topic. Masters degrees can be gamed, and some people do get them simply because it gives them more time. But difficult degrees in industries that America needs (STEM was our initial thought) we should be encouraging people in those industries to stay with a green card or some extremely long visa that isn't just chance. Determining the fields would be the hard part.

PhDs on the other hand, regardless of the field, you've contributed something unique to the collective knowledge of humanity. Instant green card, it's even dumber to kick them out.

Green cards, also aren't citizenship but are simply a step to getting there. There are many types of visas that let you work but have stipulations, especially around leaving the country. If there really is some kind of fear of people collecting citizenship after spending decades in the country and becoming highly educated, special visas with rules are always an option. But there should be a viable path to citizenship either way. We should not be kicking these people out.