I would make a few exceptions here. If you were brought here illegally as a minor and were educated here, you can apply for a student visa or apply for a work visa through an employer.
I see no compelling need to force someone who was educated at the expense of U.S. taxpayers back to their home country. As long as we paid to educate them, we might as well get something out of it.
That lets a whole host of “Latino Studies” activists hang around.
The university system should definitely NOT be a gatekeeper for this process. If it is, it will result in a final eligible population even more left wing than the average.
Having stolen an education in addition to all the other misbegotten and misappropriated wealth that belonged to Americans should not be construed as a positive in any way. In every case, a more meritorious American student was displaced to make room for them.