Most costs are outside of insurer's control anyway, regulations prevent insurance companies from telling providers how to offer care as long as the care is medically necessary and the standard of care.
I think you're also ignoring healthcare networks. This is important for two reasons.
1. The kind of supply and demand works very well for modeling commodities, but the difference in networks means it's very hard to have two completely equivalent insurance products.
2. Insurance companies can incentivize hospitals to behave in certain ways by regularly pruning those who do not behave that way.
Also, most people get their healthcare from their employer. There's not as much ability to actually switch, unless you're so fed up that you're willing to switch jobs.
besides, i think the issue is the cost of the underlying procedures - doctors charge maximum what the insurance company will pay instead of what the patient would pay. there are plenty of stories where a patient is billed $100 but if they say they don't want it out of insurance the price drops to $40 or whatever.
another elephant in the room is that you can't pick your healthcare provider if you're unconscious. this part of the US system is little more than a scam.