“We have a shortage of every kind of doctor, except for plastic surgeons and dermatologists,” said Dr. G. Richard Olds, the dean of the new medical school at the University of California, Riverside, founded in part to address the region’s doctor shortage. “We’ll have a 5,000-physician shortage in 10 years, no matter what anybody does.”
New York Times
Another option would be to loosen the definition of "physician." For example, a doctor of humanities would be qualified to conduct basic diagnostics or prescribe medicine. Obviously a DFA wouldn't crack open a chest cavity, but s/he could draw some blood and check cholesterol.
Another possibility is to train dogs and or monkeys as veterinary aids.
I should work at a damn think tank.