No, the low supply of doctors is caused by the AMA, which keeps the number of accredited medical schools low. In the 90s, they were instrumental in getting Congress to pass laws that cap the number of residencies permitted per year. Medicare pays much of residents' salaries, and the law stipulates a maximum number it will pay for, a number that was fixed in 1997, and only changed once, in 1999 (and then only for teaching hospitals in rural areas).

The US population has grown by around 25% since then, but we're still getting the same number of new practicing doctors per year that we got over 20 years ago. Doctors are overworked because we have a shortage, not for any reason inherent to their profession.