I have Kaiser insurance which is an HMO with straightforward pricing for most things. One fixed copay for doctor visit, one for specialist visit, one for outpatient care, etc. The problem is you are stuck using only Kaiser facilities and doctors.
There are benefits to continuity of facilities, though.
Anecdotally, my wife went to her regular doctor for a nominal fee at her yearly checkup. They drew blood, then asked her what hospital she wanted a follow-up diagnostic procedure to be scheduled at. She gave the one closest to us. She showed up, did the procedure, then almost a month later, we get 2 bills. One is for the blood ($1800) which, surprise, didn't go to an in-network lab despite all of our previous years' work being covered. The other bill was for the procedure ($800 if I remember correctly). If you go to the insurance website, enter her plan, enter the hospital and the procedure, it will tell you it costs something like $40. The whole system is broken, but at least these issues wouldn't have happened in a system like Kaiser.
Also anecdotally, my sister is on Kaiser in Colorado, and she has a chronic disease along with her pregnancy. They are taking very good care of her, and nothing seems to be dropped despite her having 3 physicians whom she sees regularly. I have almost no faith that if my wife gets pregnant, we'd have the same continuity in our current setup.
If an HMO got stupid amounts of marketshare it would probably fix the system naturally. It would also improve stuff like allowing HMOs to be able to better take advantage of medical data and provide better care through understanding the patient. The problem is there is too many HMOs, which makes HMOs in general less convenient.
