>>Mass immigration is a collective action by governments not a transaction between individuals. Thus the government is larger than necessary and explicitly violating the rights of individual citizens.
This isn't good reasoning. Each immigrant still has own motives and his own thoughts. A large number doesn't render these individual immigrants as a part of collective formless blob or a de facto invading army.
Consider that not all immigrants leave their home countries because of their governments. Many leave because of religious/cultural persecution from one's local community (e.g. homosexuals) or unacknowledged rights (e.g. abortion) in an otherwise secular and ostensibly stable country.
I think you're misreading Nozick. Nozick would suggest open borders, extenuating circumstances notwithstanding. The argument for closed borders would imply that any authority over a country's or state's territorial holdings would belong to the nation's government rather than its people.