Those no access to government services exist now for legal immigrants. They’re also ignored all across the country every single day. It wouldn’t be any different for the amnesty illegals.
So whats in it for them to become legal then and so why would they want to become legal? Free stuff and you don't have to pay for it (in the form of SS taxes). A win-win.
Plus, you have no obligation to the United States and you can still keep your full citizenship with your home country.