That path is too fraught with perils. Many people come to this country expecting freedom. Then they find they will be second class citizens and the resentment starts to build. I see danger in even that course.
OWK and I have a little project: an oath of citizenship needs to be reintroduced, so that those who reach maturity, regardless of place of birth and the status of the parents, would swear their consent to the constitution. Those who don't consent don't enjoy the benefits of citizenship. For example, the police department sends them a bill for the amount of police protection they consumed, and they can't vote or get elected.
Combine that with a national ID card, and you get a wholly legitimate system form the perspective of rights, although I suspect that a class of conscientious non-citizens will be quite large.