yeah, skills don't really matter for doctors, don't worry. It's just their speed
Even for the chief medical dwarf? Will he be able to make the right diagnosis at all?
The CMD doesn't need to have diagnosis skill, and they don't need to perform diagnoses. It's a pure administration job giving more information. And while that information is helpful, it's entirely optional - you can have a fully functional healthcare system without a CMD. The things you need are a hospital zone (the only administrative requirement), materials and dwarfs with the healthcare labours enabled. Like all other healthcare jobs, diagnosis is done by any dwarf who has the "diagnosis" labour active.
And yes, malpractice hasn't been a thing for years. I started playing DF 34.11, and never saw a wrong diagnosis from skill-less doctors. It's harder to say for other jobs, but no matter how low the skill, treatment never fails to put dwarfs back together again if that's at all possible. The only real trouble dwarfs can pick up during treatment are infections, and i've no idea whether skills really matter for those, untreated wounds get infected, too.
Just to reinforce the above, which is all correct.
I only started playing DF40, so I don't know about old versions, but no, there is no malpractice currently. Medical skills only affect time to perform job.
Where you can get jammed up because of low skills are patients not receiving critical care quickly enough; i.e. bleeding out. So getting them hauled to hospital, diagnosed and sutured asap. Getting wounds cleaned quickly and efficiently seems to be the big determinant on infections, which unlike RL don't seem to be all that serious anyway. I've had dwarves with infections live full normal lives, they will grab soap and bucket and head off to the well to wash themselves regularly but that's the only real effect I've seen. OTOH I don't know if cleaning supplies weren't available if their condition would get worse, but once they get an infection it never goes away.
The most important things you can do are having a properly setup and stocked hospital zone, a clean water source and dwarves available to perform the labors. So just like any other skill, use what you've got, and if you don't have anyone with the skills just pick someone to be your doctor, when you've got a patient unassign all other labors (and hope they don't immediately go off to sleep/break/party)