There’s a difference between gating certain privileges of citizenship and gating citizenship itself. I don’t think that either really works in practice, but for different reasons.
For citizenship, the biggest problem is deportation. If you aren’t a citizen, what is your residency status? Can you be deported? If you were born here, where would you be deported to?
For certain privileges of citizenship, the biggest problem is capture of the test/credential/rite of passage that you need to pass. Suppose we say that you need to graduate from high school, how long before states are fighting over adding LGBTQ and Christianity dogma to the curriculum?
Particularly where the privilege we’re gating is the right to vote, there’s a feedback loop of a slightly skewed test which skews the electorate which skews the test makers which skews the test.
I agree with your concluding point:
Let’s just get rid of citizenship, give everyone everywhere equal rights. I have three million square miles of land I can move in without needing anyone’s permission, but if I’d been born in Tuvalu I’d have less than 10. People moving from Wyoming to New York are the same phenomenon as people moving from Oaxaca to Texas.