Depending on how much independence the inspectors have they could probably turn a heck of a profit per inspector (thus being able to argue their continued existence to the legislature).

Could an inspector manage two per day? If you figure the full cost of each inspector is $150,000/year but dedicated ones could do 8 inspections at $5k each per week, there's well over $1 million/year per inspector (assuming not all inspections would be the full fine, there's travel costs per inspector, inspectors would have to spend some office/court time, etc. that would bring it down from the potential maximum of ~$1,800,000 each factoring in vacation and holidays).

Even Republicans could get behind it! "We're reducing the direct budget of the department, but authorizing it to hire additional inspectors in order to bring in additional revenue that can be utilized to bring the budget to or above its current levels." It's a cost reduction measure!

There's precedent for this; the Federal False Claims Act lets you sue on behalf of the government if you spot someone defrauding a federal program (in this case, perhaps if they take SNAP?). If your suit is succesful you get 15%-30% of the recovery for your troubles. There are "private attorney general" rules on the books at a state level too. I think it's kind of elegant, we can all see that inspections are understaffed, but non-compliance is often not that hard to spot and document. I'd propost that employees should have some whistleblower protection (and relief from NDAs and such) for building dossiers with supporting documentation of criminal fraud.

These provision are called "qui tam" from "qui tam pro domino rege quam pro se ipso in hac parte sequitur", or “who sues in this matter both for the king and for himself.”

I think they suit well with the US's history of bounty hunting, much like class action suits.

>Even Republicans could get behind it!

No, they have no actual interest in saving the government money, especially if it comes at the cost of enforcing regulations on corporations.