Bullshit.
I am making an argument for the differentiation of for profit and non-profit sectors. Insurance should be non-profit. That is NOT against capitalism.
Aren't you a lawyer, anyhow? They teach a lot of econ in law school?
I've studied lots of things over the years. I have three degrees in different fields. And I was a law professor a lot longer than I was a lawyer, and professors learn a lot of different things while they are professors. Look, it's simple: if you have any objection on the merits to what I wrote, please feel free. We can have that conversation. And then my understanding of economics will be put to the test. You can see for yourself if I'm a fraud or if I know what I'm talking about.
[edit to add: and law schools do teach econ. Every law school has at least one law & econ course, and often they have more. There are also a lot of economists who are cross-appointed with the law school, and law professors are in frequent dialogue with economists on a number of topics. That's especially true in corporate law, which was my field. I didn't teach law & econ where I taught, but I did fill in for the guy a few times when he was dealing with health problems]
When you say profits are beneficial for the need to reinvest, do you mean for health insurance in particular or is that how you see profits as a general matter? If it's the latter, I disagree. Profit motives do considerably more than provide capital for reinvestment. That's not at all to say that "greed is good" (though in that specific instance, Gordon Gekko wasn't wrong), or that the market solves all problems.
As for health insurers being non-profit, they used to be. Read about the history of Blue Cross/Blue Shield. Until 1994, all BCBS licensees had to be non-profit. They relaxed the rule in 1994, for a number of reasons. Some BCBS licensees formed bigger companies to better compete in the marketplace.
The problem with non-profits is that they don't do what people think. Well, some of the time I suppose, but non-profit status is less salutary than we might intuit. They typically do not lower prices. They just hoard cash because there is nobody to distribute to. And they pay their executives a lot of money because, again, there are no investors to push back against them.
Many states -- perhaps virtually all of them by now -- have a corporate form called a "b-corp", short for "beneficial corporation." B-corps are like non-profits v 2.0. They are allowed to write enforceable socially beneficial purposes into their charter that the board of directors must follow (this is typically not the case for corps), but they still raise capital and operate like for-profits. They aren't used all that much, but lots of corporate governance people see them as an improvement on the old technology of non-profits.