This always comes up with identification requirements for voting. It seems superficially reasonable to require them, especially if you are looking at it from abroad, or if you are pretty young. But the fact is that within living memory many American states had local policies of not recording the births of black people, and to this day there are many living black people who can't prove their own citizenship.
Unless and until every one of the fifty US states can demonstrate that they've put an ID card in the hands of virtually everybody, it won't be reasonable to condition things like education, health care, or voting on the possession of one.