There is something else that needs to be considered here. The problem isn’t “immigration” it’s “American style immigration.”
Both illegal and H1-B/TN* visas in the US create indentured servitude, and that drives down wages. H1-B/TN visas are tied directly to the specific job and the specific company, without the freedom to change jobs or companies. Dismissal from the job/company means deportation. So you have an environment where immigrants aren’t as free to negotiate or more (either up or lateral).
Illegal immigration has many of the same issues, where workers are trapped in a system that keeps them down, along with their wages.
As a personal anecdote, my wife was kept on the low end of the pay scale while she was on an H1-B, in part because she was making more than what she’d make in Canada, and in part because she wasn’t free to leave for a competitor the way her friends could (and did). During the first few years on TN/H1-B visas, we watched our wages remain stagnant while citizens say wage gains by moving laterally to other companies (or even other divisions within the company). After my wife got her greencard, her company was forced to sit up and take notice. They knew she was looking to leave, they knew she was getting calls from recruiters, they knew her friends had already left for better paying positions. Now they had to up her salary/compensation to retain her.
Other countries do better and worse at immigration, so if you’re going to have a discussion about it at least be honest.
*Show of hands who knows what a TN visa is?