‘Gigantic welfare system’? What alternate-universe US are you living in? Our welfare system is shit. We don’t even have universal healthcare!
Welfare should be to help support struggling people. Helping those who are struggling improves not only their lives, but all of society as well. This has been proven over and over again—just look at UBI programs. We should be offering more support, not less.
These people pay taxes same as legal Americans, through their employer. They should therefore get access to every American system except voting.