Quotes for...what? Even with price transparency on actual services, “I broke my leg” doesn't tell you with much specificity what services you need. And that's not even to discuss, “I'm having chest pain and dizziness”.
Sounds a lot like "my car is making a funny noise" or "my septic is backed up". Diagnosis should be cheap/free depending on how involved it is and then you get a quote for how much it will cost to fix and the quote usually includes some language like "and if X happens we'll stop work and call you/charge X to fix it as well".
Figuring out what work needs to be done based on vague descriptions by people who don't know the subject matter is what professionals do. I don't see why doctors should be held to a lower standard.
The fact is "my car is making a funny noise" or "my septic is backed up" are not life threatening situations; they are inconveniences with ready substitutes available. Health care is not a free market like car mechanics and plumbing are.
With medical there's no way to know when you got ripped off because prices vary wildly for the same services and there's no price transparency.
If I broke my leg doing something stupid you can bet your ass I'd call around and get quotes if I could. It only takes ~10min, far less than the EMT response time where I live. The problem is I can't even get quotes.
Sometimes you have no options and you get screwed but the vast majority of medical care is not people who will bleed out if they don't go to the nearest hospital ASAP. If normal services didn't cost an arm and a leg and you could reasonably shop around then healthcare and therefore health insurance wouldn't cost nearly as much because the lions share of services would be priced competitively.
Furthermore, price transparency is not incompatible with any other approach to healthcare since that information necessarily needs to exist.