I'd allow the opportunities available here be the throttle to regulate the entry of new people. When the opportunities aren't there, new migrants tend to stop coming (as during the Covid time period - when they were self-deporting). The exception to that "opportunity" rule seems to be those those cases in which the government meddles to bring in people and provide then with support (private charity does a much better job of that than does the government). The perspective you seem to be espousing is the same one the Know-Nothings used against the Irish "race", then the German "race", etc. (French, Italian, Chinese) - that they couldn't be assimilated. I fear them less that the "citizens" that are already here and who advocate that the President can unilaterally decide when Habeas and Due Process can be suspended and to whom based upon some redefinition of "Invasion" and "Rebellion".
But you didn't address that possible solution I proposed to what you consider to be the problem - the proposal being to pursue those employers who violate the law by providing jobs to those who are not legally eligible to work in the US - doing more than giving them a slap on the wrist, and actually fining them and/or imprisoning them. Cut the head off the snake. The laws for that are already on the books - just enforce them. By doing that, employers violating the law learn - that takes away the employment opportunity for those not authorized to work in the US. When all you do is go after and remove an unauthorized worker, all you've done is vacate that job positions which thereby opens the position up for the next unauthorized worker ... rinse, repeat.
Why aren't they going after the employers? It's seems like entrapment to me - the employer offers the undocumented guy a job and then ICE arrests the employee rather than the employer (and then the employer turns around and hired another undocumented guy).
And in Nashville last week,
the employers were telling their undocumented workers to go home because ICE was active in the area and the workers might be apprehended. How is that any different from the case of
Milwaukee County Circuit Judge Hannah Dugan, who was arrested for shepherding an undocumented immigrant out a back door in an attempt to avoid ICE.