What If The Border Was A Picket Line?

AITOOW wonders why illegal immigration is never cited as a cause of the supposed wage disparity of the last decades? Or for unemployment? It would seem to me that if we deducted 40 million from the supply side, we would have a surplus of job openings and employers who would have to pay more than they do now just to have a warm body. And don't tell me they would be jobs no American would do. They wouldn't do it for minimum wage. They would do it for some price. Some price the employer would have to pay or do it himself. And we all know employers are those who don't want to do the work themselves. That is why they employ in the first place.