GoodRx already does this somewhat with prescription medication, by getting pricing data on prescriptions from local pharmacies.
Perhaps, based on the GoodRx model, the opportunity is to improve price pressure on recurring procedures for patients who require ongoing dialysis treatment, dermatology care, physical therapy, etc. For emergency based care in hospitals, I still don't think it's a major net-win for consumers, as you don't care enough to ask about price when your leg is broken.