What you're suggesting is correct if you have all physicians providing exactly the same service. For instance, if each family doctor provided the same service and billed the same amount and worked the same hours, it would work fine. The reality is that medicine has evolved tremendously since the days of Marcus Welby, so that's no longer the case.
Medicine requires subspecialization. You can no longer have that one doctor who knows everything, or even a group of doctors. Radiology is a fairly specialized field. Even in radiology, in my group, we have subspecialists in neuroradiology and subspecialists in musculoskeletal or abdominal imaging.
Because the fee schedule is what it is, if they were individuals, they would all bill different amounts.