Even in non-emergency care, perfect competition requires perfect knowledge (the consumer to know medical knowledge), perfect information (knowing the exact quality of care from all competitors beforehand), rational buyers (having no preexisting biases based on irrational cognition), no barriers to entry or exit (ie, being able to switch hospitals mid stream), no network effect (the previous state...eg who does the lab work, shouldn't have an outsize influence on the subsequent, eg who does the diagnosis... See dollar auction for an extreme example https://en.m.wikipedia.org/wiki/Dollar_auction) and a variety of other fairly unachievable factors which do not apply here.
It's not a good model to structure the allocation in this particular instance, too many conditions are nearly impossible to satisfy. It's not a sensible way to design this market.
Plenty of things are pretty close to perfect competition
Grocery stores, sandwich shops, coffee houses, clothing stores, coin laundromats, circuit design, postal carriers, kitchen utensils and serving equipment, rental cars, housekeeping things like brooms and dustpans, bouquets and flowers, nuts bolts and fasteners, airlines...
Essentially anything where the brands are fairly indistinguishable and you have a hard time separating them. That's competition working.
Eyeglasses are probably one of the closest in medical. Common medicines like lactase, dextromethorphan and acetaminophen also score high.
I get mine at one of the myriad of online retailers, who seem to be outside the clutches of that corporation. There's no restrictions duties or tariffs on importing eyewear in the US and the prescription sheets are technical and specific enough to be fairly language independent.
The internet disrupts consumer by consumer and product by product, not industry by industry.
Going to a brick and mortar certainly appears cost prohibitive once you get used to paying $10 for stylish fitted pairs of prescription glasses.
Airlines are definitely not an example of perfect competition. They are the number one textbook example of oligopolistic competition leading to price discrimination. A given route between two cities only has so many airlines competing. They just have a tough time surviving because airports are monopolies (except in some major metros where there is limited competition), thus can capture most of the airlines' profits.
Good goals, but we know the current market structure is light years away from perfect.
Definitely a situation where any partial progress toward clarity and openness is a big step in the right direction. The potential for cascading changes in business practices and further reveals of all the private deals and hidden costs makes it an even better value in the future.
It's not a good model to structure the allocation in this particular instance, too many conditions are nearly impossible to satisfy. It's not a sensible way to design this market.