For a while I had individual insurance (prior to obamacare). Because it had pretty high deductibles, I would just do a private pay / cash doctor for primary care etc.
Some big wins:
NO discussion about whether something was covered or not! You want to get service, just call.
No crazy surprise bills - yes - I once tried to go to urgent care for something at the main hospital, but NO ONE would tell me what I would be charged as a cash pay client. Yes, it can be expensive to do cash pay, but with a doctor billing by the time you can basically predict / know your cost.
Service - you are paying by the hour. I never felt pressured out the door (no surprise). The service is good to great.
Convenience - I got someone close who used his downstairs as his office. Have a problem, go in and get checked out. Because you don't need the huge billing infrastructure I think you can get away with smaller office sizes. To pay for a full time biller you need a few doctors, who then need a receptionist etc etc.