I have the answer to this problem! "Really" have a "United States Public Heath Service." Young people can sign-up, and get appointments, just like the U.S. Service Academies process: deserving students get free medical school: then, after graduation, new doctors (should) must serve 6 years with "United States Public Health Department," for Government pay. Same thing an O-3, or Captain makes. But public pays a flat fee; that's really based on income, or ability to pay! The elderly, pay nothing!
The problem is: the System must be taken from the "Highly Paid Buffoons" that run the current system now! They have the gate to the profession partially closed. No free, or inexpensive system, will ever work... There're simply not enough doctors to