Sort of. There are a lot of very common misconceptions around this.
The AAMC (not AMA!) limited the number of medical school students until about ten years ago, at which point they announced an explicit goal of expanding the number of graduates from medical school.
However, this doesn't mean anything in practice[0], because the bottleneck isn't the medical school graduates - it's the residency programs. As a medical school graduate, you have an MD, but you are not actually qualified to practice medicine. That requires usually four years of training (minimum), plus several more for various specialties.
These programs are costly to run, and so hospitals that offer residency programs are funded by the federal government to do so (through Medicare). The only way to expand the number of practicing physicians in the US is to skimp on quality during training (which nobody wants to do), or to increase funding through Medicare (which nobody wants to do.
> US doctors are fewer and have more responsibilities and thus must be paid extraordinarily to work very long hours and not retire at the usual ages
They also have to be paid a hefty amount to pay off massive debt. If you see an attending physician in his 30s (or even 40s), even if he's making a respectable amount of money, there's a good chance he still has a negative net worth. The level of debt of course varies by location, specialty, and quality of education, but it's rather misleading to look at an e.g. $200K/year income for a physician and compare that to the equivalent amount in the tech industry.
[0] pun not intended, but very a propos!