Or they would just cap prices for specific procedures. Then the patient could use price transparency to see if they'd wind up with an overage bill, and consider if they'd be willing to pay the remainder (e.g. if the doctor was preferred).

Right now insurance either do cover something or they don't. That in itself is problematic. If insurance would cover a procedure up to e.g. $500 at one medical clinic why do they cover up to $0 at another? Shouldn't it be $500 here or $500 there?

Networks inherently pit you against both the insurer and healthcare provider. Instead you and your insurer should be on the same "side" against healthcare providers.