>The overwhelming majority of the money they'd be diverting by doing that would be going to health providers, not to payers and underwriters.
Yes exactly. Imagine for a moment you have a market where every payer has to pay every healthcare provider, and a free market of health care providers. It would be impossible to create a cartel of buyers raising the price.
Then imagine, say you have universal healthcare insurance. The insurance provider is capped at say, 1% profit. Since they have a monopoly, they can walk up to the healthcare providers and say "hey, please jack your costs 3x" so we can get 3x the profit. And then you can turn around and do a study and say, well insurance profits haven't changed -- and then wrongly conclude the insurance companies aren't to blame for the inflated prices, as they are only capturing 1% of the health care industry despite being responsible for 200% price increase.
I believe the nature of health insurance industry probably leaves them somewhere in a gray area in-between these two extremes, especially when you consider the insurance companies also often own under an umbrella company health care providers.