I'm ready to vote for forced transparency at all levels. I'm tired of this opaque negotiated pricing with insurance companies that manages to maximize my out-of-pocket costs.
You are correct that non-emergent care is a WAY bigger market than emergent. Most people completely ignore this. Chronic conditions like diabetes and Crohn's, end-of-life care (hospice, assisted living), dialysis, smoking cessation and weight loss, blood transfusions, most flavors of oncology (cancer treatment), knee replacements, etc.
We need way more cost discipline in non-emergent situations. Changing the perception that all care is emergent might be the single biggest thing we could do to lower healthcare costs. It would let people see that there should indeed be a market in everything from X-rays to MRIs and we could finally have a sensible conversation about cost.
For routine primary care like regular checkups or an appointment for some symptom bothering you, you absolutely are not under duress. You won't die because you took 5 minutes to choose a doctor on ZocDoc. With more transparency in costs of service, this could definitely become a market, ie "for $XX per month, get unlimited visits to our partner doctors' offices".
For emergency situations, surgeries, and things that require expensive ongoing care like cancer, you're correct in that you're under duress and can't really shop around. This is the market in which the usage of insurance makes sense, as it's a rare occurrence that would be catastrophic to pay for out of pocket for the majority of people.
I think we can do a great deal to lower cost of healthcare to Americans if we think of it in this two market approach, and handle each accordingly.