Hospitals and doctors must post their price list online.
Hospitals and doctors must disclose to each patient before any non-emergency service how much that service will cost. The disclosed cost must be consistent with the price list and must not depend on what insurance is involved.
Hospitals and doctors must not give any non-charitable discount to anyone that lowers the total amount that they charge below the listed price. (With the possible exception of Medicare.)
Hospitals and doctors must not attempt to collect more than the listed and disclosed price from any patient for any service.
In other words, if a doctor is willing to see a patient with some particular insurance plan for $100 (split between the insurer and patient however the insurer sees fit), then that doctor cannot bill a patient $300 for the same service becaues they have a different insurer.
Yes, a law like this would thoroughly invalidate the entire way that insurance contracts work right now in the US.