Instead of the government doing this (and being self-funded), why not do it commercially? Just set up thousands of personal phone numbers (honeypots) and just wait for the calls to roll in.
Naturally issues like tracking down the callers and filing mass lawsuits would generate problems the startup would have to overcome, but you'd be at an advantage because you'd have plenty of data at your disposal. Eventually you'd learn more about the branch of law that deals with these infractions and how different jurisdictions handle the cases.
What are the ethical side effects?
1. If your business became large enough, and it became a realistic outcome that telemarketers who use illegal tactics would have to pay damages like the 4k one in this article, the ROI for telemarketing may decrease to the point that it's not used any more.