True, that is the experiment to do.
It is not without ethical concern though. Unfortunately, most patients are not sufficiently informed about medicine to make a rational market choice. (Indeed, outside my specialty, I am not really either, and would seek the advice of a trusted physician friend, which is a luxury most don't have.)
For example, the PA and expert system would not reliably know when they are in over their heads and require an MD. Some subset of people would suffer serious injury or death through no fault of their own other than not having had the information necessary to allocate their funds in a manner most benefiting their interests.