The core problem with this is the implied narrative is that the citizens develop public goods and services, and the immigrants suck them all up. But in the USA, at least, that's just not true. The immigrants pay plenty of taxes. Also they are estimated to cost the economy 750 billion, but add to the economy 1 trillion. IMHO what's really going on here is the blame game.

The government steals an incredible amount of money and resources from people, but has always pacified us by giving us back some tokens in the form of public goods and services from time to time. The more they fail to deliver, the more we figure that our share of the stolen loot must be going to somebody else now, like the immigrants. But that's a lie. The government was always a failure, they created the illusion of giving something back by going into debt, buy now pay later. Well, later has now arrived.

Even if we could successfully lock out all the immigrants, it wouldn't solve our problems, just make them worse.