I have been passively following this subject for past 10 years (since I graduated college). Your suggestions are all valid and with good intent. However, 'one' group of workers these labor shops exploit are in a vicious cycle and are looking for ways to escape.
The following is typical scenario for this group: A student is enrolled in a university with average or poor CS program. There is no funding/scholarship or good on-campsu jobs. So, student works, often bending the laws, off-campus for more than 60 hours to pay for college. Obviously, education takes a backseat and somehow student graduates with huge debt. They struggle to find job and due to time restrictions on F1 visa, they are forced to find an employment and hence sign for these labor shops who give them employment letter (and apply for H1B visa) and securing students stay in US. So, initially, its a mutually beneficial arrangement.
Once workers realize they are being exploited, the struggle to get out starts.
I signed up for one of these contracting companies and they were paying me $48K when most of my fellow new graduates were making over $72K. I got out after 2.5 years, but fortunately, it was hassle free.
This is a very complex web of fraud, exploitation, bending the rules, and what not. IMO, it starts with mutual agreement/need on both sides, but descends in to the scenarios the post has brought to light.