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.