Would we pay lower rates? Auto insurance is mandatory if you want to drive. Everyone has it (well a very high percentage of drivers). There's a relatively competitive market for auto insurance. I'm not sure moving it to employers would change things all that much.

I do think that employer provided health insurance is odd, but I don't think the alternative is "free market". We have to incentivize healthy people to get insurance too, just as we have good drivers that get auto insurance. It seems like we need to make health insurance mandatory or move to universal health care. Neither are very likely in my lifetime.

Also most employers give employees the option to opt out of health insurance, and you get some amount of the money back as additional pay. Virtually no one takes this option.