However, to address your question more directly, contractors are employees as well. It's not the job site's responsibility to provide health insurance, it's their employers. Contractors still have employers, you know.
This is true for vendors, but direct 1099 contractors are self employed.
In your terms then, just let everybody be self-employed and contract them, rather than employ them. That's the same result I want, that people are responsible for themselves and making a contract with somebody to do some work for you doesn't come with any additional baggage. Just plain money for work.