I'm not sure why you call me defeatist when I merely point out why the proposed solution will solve nothing.
If I found out you were taking sugar pills for cancer, I'd point out that sugar pills do not cure cancer. Would that mean I'm ready to give up the fight against cancer?
A cop on the beat doesn't mean there'll be no crime in that beat. It means there'll be less crime.
That's kinda the way it is with solving a problem. And cancer is treated, generally, through several kinds of treatments, with the full knowledge that a quick cure is not possible. Surgery, chemo, radiation, therapy--you want to throw 'em all out, because none of them are reliably perfect?
Only citizens and lawful aliens ought to get government benefits. Requiring ID is the first step to enforcement.
I know of a non-profit free clinic in a community that requires ID for its services. They have NO illegals in their waiting room. NONE. NADA. The illegals head for the ER, where no ID is required.