I understand the concern. However, I think you still mistake my argument. I am not arguing that for-profit insurance companies are particularly benign. I am arguing that not-for-profit insurance companies are no more benign than the for-profits are. The core of your argument is that you “have seen profit incentivize abuse of the service they claim to offer.”
You have seen abuse, and you attribute it to the profit motive. I have studied this for many years — my first big study of exactly this question was over 20 years ago. I can assure you that egregrious abuse in life and death situations or quality of life situations is not at all a property just of for-profit health plans. It is built into the way we pay for healthcare.
The most egregious types of such abuse were outlawed under the Affordable Care Act. Would such abuse go away entirely under a single-payer or “Medicare for all” system? It likely would be less, as it is less today under Medicare than in the private system. But it would only truly go away if we stopped paying for healthcare in ways that make abuse of patients a strategic imperative for health plans and healthcare institutions alike.