[obstinate]

I feel like I've read some research that patient satisfaction is sometimes inversely correlated with other measures of doctors' skill. This is because the sickest patients tend to seek out the most skilled doctors, but doctors are not miracle workers. If you receive a higher fraction of people in marginal condition, you may get worse outcomes, despite having better outcomes than a similarly situated, less skilled doctor. Patients don't know this, being able to see only their own situation, and knowing only that they had a bad outcome.

There is some name for this apparent statistical paradox, but I forget what it is. In any case, the main problem with your criteria is that the "best" doctor would be one that treated only the healthiest patients. They would have low utilization, high satisfaction, good outcomes, and very good efficiency.