Very nice post, thanks! I agree that society is going to push for increased "quality assurance" in the professions - the history of medicine in the US shows that. GeographyDude mentioned the Flexner Report, which lead to implementation of actual standards in medical education and an oversight/licensing organization (AAMC).
I'm loathe to say that medicine is more important that another career or field. As you point out, programming errors can have serious and life-threatening consequences. However, in medicine the duty of care and responsibility for mistakes is much clearer and direct than say, programming. A physician practices independently and directly interacts with the patient. If I, for example, am taking care of your family member with a brain bleed and operate on the wrong side it is obvious who breached their duty to the patient (me) and who caused harm to the patient (me, again!). In programming, for example, the F35 code is probably a produced by a team which diffuses the individual responsibility, especially from the legal standpoint.
Rather than say one is more important than another, you can view it purely from an ethical viewpoint RE whether you can try again with minimal consequences. For medicine and law, "trying again" is either impossible or obscene (double jeopardy, human experimentation, etc.). By the way, this is the reason why environmental regulations and environmental laws are so important. The real world and nature gets in the way of laws of man -- we can't just unpollute or sue our way to clean air or clean water. Once it's dirty, it's dirty and it either takes extreme effort or worse is impossible to reverse.
Therefore any profession where you only get "one shot" else someone's life is ruined or lost or the effect of a mistake cannot be easily reversed, should be at a minimum restricted from amateurs. The more serious the mistake the more regulation and control and government interference there should be, to the point where if someone's life is directly affected by the skill of a single individual the entire profession should be highly regulated and its title protected by law (physicians, engineers, lawyers).
As an aside lack of "one shot" and regulation is the reason why the IT field is unique and attractive for entrepreneurs... low barrier to entry (assuming you are a top-notch programmer that is) and no regulation means you can try and try again to make that website or app or enterprise software with little consequence to human life and limb. Try that with other fields and you will either go bankrupt or kill someone.