You keep misinterpreting "how much [a doctor] themselves will charge for something" as "patient's out-of-pocket cost". I'm certainly not asking for the doctor to get involved between the patient and their health plan [0], but rather what the doctor charges, regardless of who might pay. In other words, the straightforwardly-legible prices that exist in every other market - even markets where insurance companies often pay (eg auto repair).

I don't know the specific legal details that allow doctors to make up these post-facto bills (often fraudulent) and send them to patients, but I feel it's probably at the state level rather than federal. Also the big problem with regulatory capture is that businesses paying off politicians makes that kind of citizen feedback meaningless.

[0] in fact I think another good angle of reform would be "if a patient has a health plan, providers are prohibited from billing the patient directly". Any copays, outstanding balances, etc should flow through the health plan.