Only illegal migrants aren't covered, legal ones are. If you make it available to everyone regardless of their legality to be on the soil you open up a whole bunch of other issues
Canada largely avoids this problem by not allowing a subset of illegal people to exist in the country. Canadians are polite, but working in canada without some sort of legal status is far harder than in the US. They have lots of immigrants, but vanishingly few illegal ones in comparison to the US.
