The first glaringly obvious problem is a growing, aging, populace. Baby boomers are getting older and about 1/3 of doctors are over 65. What happens when they retire?
It should be noted that when I say that's the problem, I don't mean a lack of doctors, it's a lack of other medical professionals. The problem isn't and undermanned system, it's an inefficient system. We need to expand the use of nurse practitioners and physicians assistants and not have them forced to be under a doctor. NPs and PAs are limited by rules, not their abilities.
In 2014, the Institute of Medicine did a study and found that we don't really have a shortage of doctors.
https://www.nap.edu/resource/18754/GME-RB.pdf
The entire health system needs an overhaul that is conducive to a free market system. When doctors have to hire a team of people just to file paperwork, that's a problem.
When people are forced to go to the ER on a Sunday because no doctor is available, that's a problem. We need more places like a minute clinic and less ER visits.
Continuing to expand Medicare and Medicaid is not going to work. Government taking control of health care surely isn't going to work (it hasn't yet).
We need FDA approval times to be faster. On average, it takes 10 years for a drug to make it to market.
We need less government intervention and more innovation.
We need more doctors spread around. When Medicare reimburses at higher rates in and near cities, that's where doctors will go. More rural areas then experience a shortage.
We have great specialists. But not enough general doctors. That's because specialists can make a TON more money.
It could be due to tuition as well. By time you finish med school, you're a quarter million dollars in debt, still have years of residency left, and are making $52,000 a year. It's no wonder there are tons of specialty doctors.
The problem is, none of this is easy and the longer we go, the more people will be questioning the system we have, unfortunately.