That's union socialists thinking where everyone is just a mathematical unit, where everyone has the exact same value and the only way a man can demand more for his labor is if he can eliminate competition from all the other units.
Employers don't care how many "bodies" are out there. The owner of a collision shop wants the best bodymen he can get and he will pay what he can afford to get someone who can take a brand new car from a dealership, repaint it a more popular color and return it to the dealership in such perfect condition that the dealership can sell it without the buyer ever knowing that it wasn't a factory paint job. He doesn't care how many "units" are out there mowing lawns.
A construction roofing contractor has deadlines to meet and needs experienced, skilled, dependable roofers who can keep up with the builders' schedule. He doesn't care how many "units" of landfill workers are out there.
There are very few jobs where skill and experience aren't important, and for those we have minimum wage laws.
Mathematics really does play here. And with more bodies in a given category, wages will tend to sink where illegals can compete, towards the minimum wage, assuming the jobs are on the books. The stats simply bear this out. The inequality of wages has grown very substantially since illegal immigration gained real momentum. No sweat off my back, but it has changed the social landscape in my neck of the woods. High wage Anglos push paper, often very high value added paper, and low wage folks who work with their muscles tend to be Hispanic, with a huge wage gap. Lower middle class and working class Anglos have to a substantial extent, decamped.