Brownlee proposes the alternative of paying doctors a salary, based on the number of patients that they see. However, I would argue that this would create the opposite incentive. Under a capitation based compensation system, a doctor would want to see as few sick patients as possible, because each one takes a lot of time. You will be paid more if you have a large roster of healthy patients than if you have a small roster of sick ones.
As an economist, I believe that there is no perfect way to compensate doctors. I would like to see experiments tried with different systems than the one we use today, to see if they improve things. But I would definitely not say that shifting to a capitation based salary system would bring nirvana.
The book is a journalist's villains-and-victims story. The good news is that her ideas of villains and heroes are a bit unconventional.