Commenter Spencer says:
This is the biggest problem I have with libertarians. Why you always seem to think you improve standards of living with cheap labor is beyond me.
If the relative price of something is cheap you will use more of it. Consequently if you keep the price of labor low through immigration you encourage labor intensive production process. This does not raise living standards. If you want to raise living standards you want to shift the production process towards a more capital intensive process where the additional capital per worker allows them to be more productive and raise living standards.
That would seem to make closing the borders a win: Americans get higher wages and more automation. But it assumes that the immigrants themselves have absolutely no moral standing. Their lives aren't made better by the fact that America has automatic fruit picking machines.