This would also allow industry to focus on what industry does which is make money. They no longer would have to spend on expensive Cadillac health care plans in order to compete for employees. Governments job is to keep its populace safe and healthy, that is not the job of private industry.
The only reason we don't have this is due to lobbyists.
Retirement makes sense as this is your source of income. I feel that company resources would be better spent elsewhere than on healthcare.
This would, of course, require universal healthcare or direct market healthcare. This would help new businesses thrive, especially the "mom and pop" types.
I guess I am jaded on this as my parents lost their business when I was growing up due mainly to the cost of healthcare. Not all companies have monolithic budgets.
I doubt most Fortune 500 employees would support turning their company plans into some medicare-for-all. Next step would be turning Social Security over to Goldman Sachs.
Getting health insurance, whether public or private, out of the hands of employers is probably the single best thing that could be done for working conditions in America.
One potential issue is that I think there are fewer legal requirements, but competitive employers already provide benefits that exceed the legal minima.