I say this with respect- but that's a bit of an 'ivory tower intellectual' position that doesn't consider how things work in the real world.
I'm not just talking about ABUSE, which DoL should prevent. I'm talking about personal drive and demand of upward mobility.
For example- let's say you have a company committed to following the rules, who will pay what the market demands and treats workers with respect. You have two candidates for a job. One is an immigrant- lives in a lower end neighborhood, but is thrilled he can feed his family 'only' working 60 hours a week and his daughter can walk to school without being abducted and raped. He'll do the job as long as it's offered for $10/hr and be thrilled at that. The other is an American who wants upward mobility, they want to do this job for 1-3 years max before being promoted to something bigger, and if he doesn't get promotion he will leave.
There's no abuse and nothing illegal happening here. Just supply and demand.
If you're the corporation, which person do you hire?
Almost every company I know would hire the immigrant, because he'll work hard, he's thankful to have the job, his lower-middle-class lifestyle is better than what he had before so he has no need to demand more.
But if the immigrant isn't there, they'll have to hire the other guy, have to pay him more, have to provide promotion opportunities or train new workers when he finds something better.
There's nothing for department of labor to do there, because there's no violations happening. This isn't a legal problem. It's a socioeconomic one. No government agency can force the immigrant to demand higher wages, or force the company to pay above minimum wage.
(Minimum wage should probably be $10-$15 today, but that's a separate issue).
And that’s all without the macro economic point of view that points out having more consumers in your country means more economic activity which means more jobs.
That only holds if those consumers have disposable income. And those consumers only have disposable income if they're demanding wages high enough to afford luxuries.
If you have workers who will settle for very low wages, that depresses wages across the board. That means less disposable income for everyone, and can mean overall LESS economic activity because wages will decrease, consumer spending will drop, and money will accumulate as profits for large companies that reap higher profits from overall depressed wages (sound familiar?). I'm not blaming immigrants for that (I blame Congress and the absurdly low minimum wage) but the point stands.
Bottom line- if you have two groups of people, one says 'I'm happy with what I get' the other says 'I want more', more of the first group means less wages for both groups. Supply and demand.
Because the man you don't like got elected we should shred the 1st Amendment right of free expression? Or do I misunderstand you?