My father was an anesthesiologist (who retired in good standing), and I remember him telling me a case he read about a Caesarean section. The surgeon was using an electrocautery pen to sear closed the ends of blood vessels. The surgeon set down the pen on the surgical cart, lifted the baby out, set the baby on the cart, and the baby's heel touched the pen. Now the baby has a small scar on the bottom of his/her heel for life. The parents sued the surgeon, the cart nurse overseeing the cart, and the anesthesiologist was close to the surgical cart. All 3 defendants settled out of court, since babies almost always win jury cases against rich doctors, regardless of merit.
The litigant's lawyer would almost certainly bring up a below median survival rate as evidence of a pattern of gross incompetence.
Also, of course, in the U.S., I believe only governments are immune to lawsuits (sovereign immunity) without their consent. The courts have consistently ruled that many rights, including the right to sue, cannot be legally waived by contract. In a similar way, if you sell yourself into slavery by entering into a contract that waives your right against unlawful detention, that contract cannot be legally enforced.
My grandfather was an anesthesiologist. My dad was an anesthesiologist (and did well enough on the MCAT to go to med school after 3 years of undergrad... practiced medicine without an undergrad degree... med school is too competitive today to do such a thing). I was a good student: I graduated from MIT. However, my brother and I saw all of the BS and stress (anesthesiologists have a high suicide rate) and constantly rotating sleep/work shifts and both went into engineering.
There are medical boards to remove incompetent doctors, but those influence jury trials primarily through submissions of findings as evidence for consideration by juries. A good lawyer will portray medical boards as a bunch of doctors biased against passing judgement on fellow doctors.
This is entirely reasonable and I cannot imagine how you could have a medical system where you can't?
What do you do if your surgeon operates drunk and kills you? Hope that a bunch of other doctors don't close ranks and protect their own at your expense? Why would anyone have any faith in their fellow man. People are terrible.
Can you see that this introduces a level of recklessness that isn't present in the parents question? Parent is asking about normal death by medical error. That's likely to have complex causes and is rarely as simple as "doctor was negligent".
But assuming that a doctor does kill someone: most relatives don't want a pay out. They want to know that this mistake won't happen again; that people and the orgnisation have learnt from the death; and they want an explanation of what went wrong along with an apology.