If we didn't have the illegal immigrants, we would have been further along with really cheap labor: robots. Lack of cheap human labor creates demand for automation.
I'd much rather have that than have the US be overrun by invaders who have no regard for our laws or culture.
Besides that, I suspect something unintended might happen. People will develop a desire for simpler hand-made things to fill the void left by computers dehumanizaing everything. It'll create demand for craftsmen, home project skills, restaurants that are more personalized. I think you're already seeing that in some environments. Add to that wages for the population increasing when there is no unnecessary competition from invaders, and the technology won't be anywhere near the threat that the invasion is.
If it upsets Chamber of Commerce types and other cheap labor elitists, that's just icing on the cake.
You are so right. Japan and some South American countries are beating the pants off us in automotive assembly and other tech's because they are not forbidden by unions to use advanced robotics.