The problem with the idea of "shopping for care" is two-fold. First and foremost, a significant portion of care, especially the more expensive types of care, become needed suddenly and unexpectedly, so there is little to no chance for comparison shopping. Secondly, individuals just don't have the economic clout needed to extract price concessions from the oligarchic hospital industry. Personally, I think the best reform one could make in restructuring how our health-care system works would be to require that health insurance be run on a non-profit model. That would insure that insurance works on behalf of the insured and provide the needed counterweight to the hospital industry.
Agreed.
I also think one of the major ironies of the ACA was the way in which the "mandate" was made a lightning rod. The problem with the mandate was not that it was too onerous but that it was too toothless. If young folks didn't buy insurance, and didn't pay the fee for not buying insurance, the IRS had no authority to take them to court for the delinquency. So, young people didn't buy in and the state exchange markets suffered as a result because the coverage in many cases could no longer be financed, and insurance companies pulled their particiaption in many places, or raised their premiums and increase the amounts of subsidies customers required. In the '94 Senate Republican bill that was the basic origin of most of the ACA, the individual and employer mandates were stronger than in the ACA, which would make the whole framework easier to finance.
But, in the big picture, I agree; having insurance run by people who are trying to satisfy investors skews the motivations that go onto health insurance specifically. Non-profit private insurers work much better, I think.