You can shop around for health insurance.

I cannot effectively shop around for health insurance because, as an individual consumer, I am in the minority of insurance consumers. Most insurance consumers are businesses. (Several agents have told me that.) Thus, there is no incentive for insurance companies to lower prices to attract individuals. If all consumers were individuals (or groups of individuals, such as professional societies) the market would be different.

Everybody NEEDS health care.

True. However, everybody does NOT NEED health INSURANCE. I went without insurance for most of my college years.

I mean, again, as a profit-driven business, why would I insure someone for $FOO/month when their calculated cost is $FOO*2/month?

You would insure them because you can get enough customers with a calculated cost < $FOO/month to cover those customers with a calculate cost of $FOO*2/month. That's how insurance has always worked. Other businesses that have to manage cost v. risk work in a similar manner.

Collective bargaining for health insurance is the only way to cover the cost of those types.

Wrong. I have seen some wonderful things done by charities, particularly for children in the Atlanta area.

What's wrong with auto insurance being provided by an employer?

We would have the same market for car insurance that we have for health insurance. It would be skewed in favor of large volume consumers (businesses).

If it spread the risk across a broader range of people, why is that bad?

Spreading risk is part of the insurance business and is accomplished by getting more customers. Employer provided insurance is not required to spread risk.

Again, I understand that for the folks who are considered low risk in the first place, it ends up potentially increasing their rates.

You have that backwards. The more the risk is spread, the lower rates should be for everyone. (I have seen it happen.)

But, again, so what?

Somehow I think  you would not be so cavalier if your rates were increased.