All this actually presupposes that you can get rid of illegal immigrants, otherwise anyone who does not get the BLS (for whatever reason) will essentially earn

All this actually presupposes that you can get rid of illegal immigrants, otherwise anyone who does not get the BLS (for whatever reason) will essentially earn a fraction of the money the recipients get. Why? Well for one thing his wages by means of taxation have to pay the BLS to everyone else. Secondly if he has children, they probably don't get BLS either, and he has to pay for them out of a minimum wage, too, which a BLS recipient doesn't need to do.