General health care should be provided based solely on current geographic location (i.e., hospitals/clinics should be subsidized by local/maybe state government) because this would inhibit the spread of disease. This is a simple matter of the public interest.
Drivers licenses should only be available to citizens, resident aliens, and (shorter-term) to verified legal nonresident aliens. Providing them to illegal aliens - completely bypassing documentation - would simply make it all too easy to quickly establish multiple legal identities. Allowing people to get legitimate drivers licenses would render the "other use" (i.e. as state-defined primary means of identification) essentially moot. Again, it is a simple matter of the public interest.
Education is important, but it is provided as a function of the political unit (I would say "State", but I refer to the generic meaning, and not the more specific meaning common, for instance, in the United States), which, theoretically, is an abstraction of the citizenry. As an abstraction of the citizenry, the State/political unit's primary responsibility is to the citizenry which it represents. Mechanisms already exist which have the aim of allowing one to join the citizenry, so one can hardly claim exclusion from the benefits of the State if one does not become a member of the State. We're not talking about helots here, we're talking about people who legally are (typically) members of other States/political units. England has no responsibility to provide education to Japan, nor Japan to England. Their responsibilities are to their own people.
*edit* Just thought to mention - technically, if a child is born in the U.S., Jus Solis provisions apply and the child can claim U.S. citizenship. */edit*