When the immigrants have equal rights and they get the job, that's a fair meritocracy. Immigrants don't automatically like getting paid less or work in a toxic environment or live in a shitty house, they endure it due to the restrictions on their rights to move and work. In other word, Immigrants are not people who don't know better.
When you limit the immigration, that's like the taxi medallion system which creates a fake shortage which benefits only the medallion holders. You end up with shitty taxis.
There's nothing wrong to be paid fair market wage. I wish we can just abolish this medallion system altogether, people shouldn't be asking for permission to work and travel. This must be an universal human right.