I would partially disagree with this assertion (immigrants are clearly very constrained in their job mobility, and their wages are correspondingly suppressed) but what TFA and other similar studies and history show, it's not like wages increase for native employees with lower immigration. Typically what happens is that there just aren't enough people to do the work, and so the work just doesn't get done, which is why businesses just don't grow.

Sometimes the economics just don't work out. Relevant berry-related example, California farmers often have had to let entire years' worth of strawberries rot in the field when they could not find enough farmhands to pick them. And they did try raising wages and perks: https://www.ucdavis.edu/food/news/california-farmers-have-ra...

But sometimes even with the right economics there just are not enough workers. TFA gels with my experience working in Tech in the US for almost 2 decades, conducting countless interviews for positions that I know paid very well, and just not finding enough qualified candidates regardless of visa status, which constantly put significant constraints on our roadmaps.