Of course, the obvious drawback to not paying doctors on the basis of the services they provide is, well, what is then their incentive to do anything? Sure, you could pay them based on some stable of patients that they manage, but a fixed salary seems to encourage doing as little as possible to earn that salary.
Well, of course, you could try paying the doctors based on the health of that stable of patients. This will encourage good preventative care. It will also encourage doctors to not take on new patients who are likely to be sick, and it will mean doctors in richer areas make much more money (probably already true). I suppose you could pay doctors based on how their patients fare relative to expectations (the way some school systems try to) based on their socioeconomic status and starting health, but this gets into a lot of games.
And then, I enjoyed David Goldhill's article "How American Health Care Killed My Father" which argues (though I can't do it justice with a single quote)
The most important single step we can take toward truly reforming our system is to move away from comprehensive health insurance as the single model for financing care. And a guiding principle of any reform should be to put the consumer, not the insurer or the government, at the center of the system. I believe if the government took on the goal of better supporting consumers—by bringing greater transparency and competition to the health-care industry, and by directly subsidizing those who can’t afford care—we’d find that consumers could buy much more of their care directly than we might initially think, and that over time we’d see better care and better service, at lower cost, as a result.Goldhill's point is that a big problem is that patients don't really pay for their own care and, if you happen to be paying for your own care, it's impossible to find out what anything will cost anyway. There is really no way for consumers to comparison shop or determine what anything is worth to them personally.
But returning to the issue of doctor pay, which is an open question whether we have insurance or government footing the bill. My best guess is that different doctors respond differently to different incentives and that, assuming one system doesn't categorically pay better than another, it would be good to have different systems (some fee-for-service, some fee-for-patient, some fee-for-incident, and so on) and let each doctor choose the system that lets them do their best work.