"Just because the state performs a function, it does not automatically invalidate the function."

Agreed. Bastiat discussed this in 1850.

"Socialism, like the ancient ideas from which it springs, confuses the distinction between government and society. As a result of this, every time we object to a thing being done by government, the socialists conclude that we object to its being done at all. We disapprove of state education. Then the socialists say that we are opposed to any education. We object to a state religion. Then the socialists say that we want no religion at all. We object to a state-enforced equality. Then they say that we are against equality. And so on, and so on. It is as if the socialists were to accuse us of not wanting persons to eat because we do not want the state to raise grain."

However, you lose the plot as soon as you continue your argument. National borders are not analogous to property lines. Other people are not your property. Government does not represent you. Whether the allegations of immigrant criminality are true or not (and statistically it appears they are less likely to be criminal than 'MURKANS) the fact remains that government is inherently criminal in every aspect of its operation. And if you reject the legitimacy of all usurped centralized power, there is no danger of marxists siezing it.

The allegations that they will be welfare whores are not supported by statistics at all, and the root problem of the welfare state is the same state apparatus that claims we need to fuss about its borders.