There are a few relatively commodity items you have mentioned, flu shots for one, mammogram possibly another, but for > 65% of patients those are already covered at extremely low/no cost. Yes, there is room to help the remaining 35%.

As you get into xray, clinical laboratory, other imaging things become very complicated where the order from the provider is commonly bound to a particular facility. Trying to get a provider to write an MRI order to a facility they have not worked with before is often a multi-day process fraught with error due to complexity in the order itself. Most patients cannot get their providers office in active communication long enough to even try it. For procedures there is an exponential explosion in complexity. Electives are really, really complex. A birth or a hip replacement is not the same thing across facilities so how do you compare code level pricing?

With drugs GoodRX has produced excellent results for patients. I think that works so well because overwhelmingly drugs are commodity goods.

I do see an oppourtunity because health systems spend a tremendous amount on patient acquisition currently but I am having a difficult time seeing the dots connect into pricing decisions by patients.