Casting the patient doctor relationship in terms of power dynamics is a bogus sociological construct divorced from reality. The true division of power is between those who fund healthcare and those who receive it, I would start there if you think things need to be improved.
To say there is no power dynamic between patient and doctor is wildly ignorant. There obviously is one, even if the patient is not paying the doctor directly for their services. Not sure when (if?) you went to medical school, but this is taught to all medical graduates. The field of medical ethics exists for a reason.
Patient can of course bring whoever they want into the circle. The problem is the intrusions that neither healthcare provider nor patient want.
But sure, uninvited third parties shouldn't butt their head in often, except for the occasional regulator.