So the assertion seems to be: the “consent of the governed” justification for democratic power is called into question if you allow the voting power of existing voters to be diluted by the introduction of new voters.
OK, fair enough, there’s a certain theoretical cleanness there.
Shall we trade tight governmental restriction of immigration for tight governmental restriction of procreation?
I think the answer is, “this is what Westphalianism is for”.
This works only if the Westphalian state is a natural unit in terms of the consent of its constituent voters. I think history has made it abundantly clear that this is completely untrue.