You could simply document the immigrants and incorporate them into large labor coalitions auctioning their work at market rates.

Instead, we have a system of paying workers under-the-table at below market rates, while using their illegal status as leverage to prevent them from negotiating for better pay.

So you need a legal system for migration before you can get higher wages and worker protections. Otherwise, you’ll always have a reserve army of scabs in the form of undocumented residents.