The supply of physicians is primarily restricted by limits on federal government funding for residency slots in teaching hospitals. Every year there are students who graduate from medical school but are unable to practice medicine because they can't get matched to a residency program.
The supply of lawyers isn't restricted at all, as shown by stagnant or falling median wages. Almost anyone who wants to become a lawyer can enroll in one of the "third tier toilet" private law schools, and states don't impose any limits on the number of law school graduates allowed to take the Bar exam.
I'm surprised to hear the AMA has no influence over the size of residency funding, but if that's what you're saying, I'll take your word for it.
The supply of lawyers is restricted through onerous education and licensing requirements. You could argue that the fall in wages means they are no longer as effective in controlling supply. But if you think the supply "isn't restricted at all" I encourage you to start offering legal advice for money and let me know how that goes for you.
The AMA has been advocating for increased graduate medical education funding. I suppose they have some influence, but apparently not enough to convince Congress to boost funding enough to meet the demand.
I don't see anything particularly onerous about education and licensing requirements for lawyers. A sufficiently motivated student can complete law school and pass the Bar exam in a few years. So in practice there's no significant restriction on supply.
The supply of lawyers isn't restricted at all, as shown by stagnant or falling median wages. Almost anyone who wants to become a lawyer can enroll in one of the "third tier toilet" private law schools, and states don't impose any limits on the number of law school graduates allowed to take the Bar exam.