Career healthtech worker; opinions are my own; focusing only on the provider-specific questions you're asking:
Biggest problem (w.r.t. provider overwork and availability) is regulatory capture by AMA and hospital groups. The AMA has for decades induced an artificial shortage of MDs by limiting the number of available residency slots. In particular, there's an acute shortage of slots for primary care providers (gen practice, family med, internal medicine, OBGYN) - which combined with financial incentive, leads to an oversupply of specialists.
AMA is also very assertive about keeping alternative providers (e.g. nurse practitioners) from having the rights to perform certain procedures - again as a form of financial protectionism. I'm picking the worst possible example, because it goes wrong all the time, but in many LatAm countries for example, routine x-rays and ultrasounds are often read by technologists rather than radiologists. Broadly speaking, there's a chilling effect of provider liability, in that your PCP may not be a dermatologist, so instead of doing a mole screen themselves during your annual office visit, they send you for a specialist visit instead of doing it in house (to avoid the unlikely chance they miss something subtle the derm might've caught) - costing more money, fueling the oversupply of specialty care, and letting the "general" skills of GPs atrophy even further.
TLDR: The American Medical Association kills people.