I am medically self-insured, to an extent. I am responsible for a $20,000 two-year deductible on all medical expenses, and after that my quite inexpensive major medical (aka "catastrophic") insurance kicks in.
Much to my surprise, it turns out that many both large and small businesses use this same model, as do many large unions. In most of those cases, however, the business or union covers the costs of the deductible, and brand-name insurance companies administer the policies for a fee.
From this article: The Attack on Self-Insurance - Liberals want to rewrite Erisa to save ObamaCare:
Today a record 61% of covered workers are in a self-insured plan,
according to the Kaiser Family Foundation's 2013 survey, up from 49% in
2000.
Democrats clearly want, as a step towards single-payer, one-size-fits-all medical insurance controlled by them. As usual, they want control "for our own good", of course.
My approach would be to deregulate medical insurance, and to let a million flowers bloom.