The five largest health insurance providers in the U.S. by market share are UnitedHealthGroup, Kaiser, Anthem, Aetna, and Humana. Of those five, all but Kaiser are strictly for-profit, and Kaiser is a consortium of for-profit and non-profit entities.

Equating risk-bearing providers and health insurance companies for the purposes of arguing that health insurance isn't insurance might as well be tautological. Sure, blueberry pancakes aren't really pancakes if you include blueberry muffins in the category of blueberry pancakes, but who cares?