From the standpoint of a practitioner, the populations served and burdens (and rewards, even apart from financial) are substantially different. To combine them would probably reduce interest of physician participation in serving the populations. A couple of the issues. For populations that are not billed directly for their services, a lot of times their relationship is with a clinic and not, to some extent, an individual provider. For instance, a 'retired' Army orthopedist may close his private practice and work 20 hours a week at a VA hospital. Almost all medical school practices are of the type of an institutional relationship. So potential frustrations about rate of individual procedure payment or compliance with appointments are obviated by salary and opportunities to participate in supervision, research, and educational conferences. For a purely private practitioner, the rule may be 'the first third of the patients you see, you pay for your overhead; the second third, you keep body and soul together; and, the last third, you make money.' Medicaid's payments and bureaucratic impediments to achieving work or payment impedes you from achieving any of that; so treatment may be done, to the extent it is, in the interest of treating 'the broad range of patients.'
In the case of patients seen through an institution, it is the institution that conveys the 'price mechanism' to use the language of a critic of socialism.