I think you're missing my point. My point isn't that those situations don't exist, my point is that they don't make up the majority of situations in healthcare, nor do they make up the majority of healthcare expenditures.
> And I think that you are wrong, particularly when you consider this based on dollars billed by emergency rooms, not patients seen by emergency rooms.
The statistics are that all emergency care expenditures totaled accounts for about 2% of all medical expenditures, or in any case no more than 10% depending on who is reporting and calculating [1]. And, not all emergency room visits are emergencies by far [2] and many patients are swayed by things like advertisements for emergency rooms.
Who is talking about all medical expenditures? I am talking only about emergency room visits.
1) Ads for emergency rooms function as ads for hospitals in general. People in need of non-critical care will naturally be influenced by ads that depict a high quality of care for emergencies. The existence of ads for emergency rooms therefore tell us little.
2) "Real" emergencies will almost certainly be more expensive than "non"-emergencies. They are going to charge more to sew your hand back on than to give your kid some coughdrops.
3) "Non"-emergencies, as perceived by a doctor, are not the same as "non"-emergencies, as perceived by patients. The mother frantically driving her kid with a broken arm to the hospital is going to consider the situation far more urgent than a doctor would. In these cases, people are not going to act with price sensitivity, even though they could, strictly speaking.
> Who is talking about all medical expenditures? I am talking only about emergency room visits.
I said "my point is that [those situations] don't make up the majority of situations in healthcare" and you said "And I think that you are wrong, particularly when you consider this based on dollars billed by emergency rooms". I don't get the point of looking at a percentage of emergency-related dollars billed in emergency room visits. My point is that if less than ten percent of all medical expenditures are related to the type of emergencies where (to quote OP) you are "bleeding out in the middle of a street or who are delirious from fever [and] won't be acting with price sensitivity.", then that type of situation is not a primary driver of medical costs in the US, nor is it the most important factor to consider when deciding how our medical system should be run. A huge portion of health care expenditures are of the type where a person would act on price.
Also, I get the impression that "emergency care" omits emergency-related care. If you receive "emergency care" its not unreasonable to assume you may well need follow up - and that follow up could easily end up costing a lot more than the original incidents "emergency care". But that later care is often closely tied to the initial incident. Moving patients around and/or switching doctors often isn't easy nor necessarily safe.
In short: Non-emergency care doesn't necessarily mean care where you can flexibly and easily choose your care provider.