Does the military pay for one's education, if one has the needed academic grades, and then commits to an enlistment upon becoming an MD?
Anyway, with HMO's, and fewer private practices, many doctors are not even earning large annual amounts of money. So, paying off a loan, based on more nominal earnings, can be a demotivator to a medical career.
Then there are foreign medical schools. Not everyone's preference.
So, the problem, in my opinion, is not who gets to play doctor, but whether there are enough doctors to treat all the patients in society. You might have put the emphasis on the wrong syl-la-ble?
But, if you want to focus on the poorer intelligent child that has been telling adults, since kindergarten, that he/she wants to succor the sick and lame, then why must society treat the child's wishes with such concern?
The expedient answer, in my opinion, is to have physician's assistants (ex-nurses perhaps) do much of the work that doctors used to do, and the doctor (that came from a well-to-do family) can sit like an all knowing sage in his/her office giving instructions to the physician assistants. Naturally, some of the duties of the physician assistants might include dutes such as getting the doctor's coffee, lunch, etc., but that makes sense, since the doctor did come from a well-to-do family, which correlates to one's "social class," and the physician assistants came from a more middle-class background, at best, and that correlates with a lesser "social class." So, society maintains it homeostasis, that being the real important focus of the dilemma, in my opinion.
The concern you voiced in your post , regarding the inequity of everyone that might be qualified to be a doctor, may not be able to afford the education, reflects, in my opinion, the false-premise that everyone should have the same opportunity in society. That goes counter to the reality to all the westerns I saw as a child on (black and white) tv, where there were families owning great swaths of land (aka, Bonanza), and today their descendants can afford to go to medical school, etc. In other words, the early bird (to the U.S.) catches the proverbial worm. That is how the U.S. evolved. To change it now, just treats those well-heeled families and their ancestors that died from cholera, typhus, smallpox, with a flippancy, in my opinion. Oh yes, their ancestors also died in wars that my ancestors did not even know were occurring. So, they rightly earned their dominant position in society, in my opinion. Otherwise, I would just be an upstart wanting to gain an advantage that I would not have earned, in my opinion.