it just doesn't work that way. there's this thing called equality before the law, or something.
this sort of thing has been tried and US state and local governments are generally not allowed, by federal law, to deny the most expensive benefits and services to immigrants. it's, like, the US constitution and stuff.
note that educational services (i.e. schools) are a very large part of state budgets. like, sometimes the largest single component of a state budget. so the big savings would have to come from that sort of service denial, which again, is not constitutional.