The other question that is rarely asked, is why isn't much more of the training and services restricted to physicians expanded to other professionals? That is, it's not just "why aren't there more physicians?" but also "why do we need a physician for X?"
There are lots of provider types who could easily expand their scope of practice with additional training, and who are currently prepared to do so. The AMA lobbies heavily against any attempts to do so all the time, every year. Pharmacists, PAs, dentists, optometrists, psychologists, nurses, ... the list goes on and on. Every year they lobby heavily to just have the opportunity to offer more services, and more services independently, the AMA fights back against it in lobbying, and politicians respond to it.
The crisis in some ways highlights how absurd this is. Right now I know of many med schools whose in-class training is about 1.5 years, and some are trying to make that 1 year. The rest is studying for licensing exams and clerkships. Now many of these schools are graduating them early to help with the pandemic.
Compare that with PAs, who often are required to have substantial medical clinical experience before starting their programs. Then they do... 1.5 years of coursework and about .5 years of clerkships before going on and then... practicing under the supervision of an MD. So, then, what's the difference between a new MD and a PA with an extra 1.5-2 years of supervised experience, especially given that extra 1.5-2 years of experience is probably more independent than what the med student gets?
The current model is absurd, and at some level I have no sympathy for complaints that hospitals are understaffed right now. This is solely the fault of the AMA and their lobbies at some level. Many services could be offloaded onto other providers, who could easily expand the scope of what they offer, especially in the middle of a public health crisis per se. There could also be a much greater diversity of training routes than undergrad -> MD -> specialty (just for example, undergrad -> specialty doctoral/professional degree -> expanded training).