You don't even have to make it illegal for your employer to pay your insurance premium, just take away the tax deduction and watch how fast your employer stops paying.
I suspect they still would provide it, because it would be a competitive advantage. I get better rates on health insurance through my employer than I could get on my own, presumably because the average working person is cheaper to care for than the average person. So, my company (and most companies) would still find an advantage in hiring if they offered health care. (I'm assuming above that you're talking about taking away the employee tax advantage for this insurance (the avoidance of personal income tax on it). It occurs to me at the end of my reply that you might consider treating it as a non-business expense and that the company would have to pay corporate income tax on the money they use to buy health insurance. I agree that doing that is a big hammer, but it also seems like a terrible idea. If the company has a legitimate business purpose in spending its money that way, namely to better compete for employees, then it's a legitimate business expense, IMO. Trying to enforce social change via the tax code rarely results in precisely the "clean" outcome that people lobbying for those changes intend, or purport to intend.)