Most companies would love to do away with the expense of health insurance and all of the administrative headaches and costs that come with it. But since most full-time white collar jobs offer health insurance, changing jobs might change your coverage some but won't leave you insuranceless. Now if you want to go out on your own or create/work at a startup, health insurance can be a big issue.
Big companies already have the HR staff to deal with health insurance. It’s in their interest to keep health insurance tied up with employment, as it gives them an advantage over small business and individuals, because individuals who work for small businesses that don’t offer health insurance have to pay for it with post tax dollars.