How do you envision a national-wide health care system based on private non-profit organizations? I can't imagine that. For me it looks like there are only two variants: either profitable private business, or government tax-funded program. If the regulation takes away private insurer's profits, insurer will find better use for his money.

In reality, though, they will not sacrifice their profits, at least initially. They will raise premiums. Government will probably want to cap premiums in order to protect public, insurers will come up with some other way to transfer expenses to customers, and so on. Very entertaining process, especially from a vantage point of a guy who pays for it.