Power
Pain is the great equalizer of human beings. Rich and poor alike can be reduced to weeping, writhing, helpless shells of their former selves if the pain is severe enough.
Enter the savior, the doctor who can reduce or eliminate pain. That's the anesthesiologist. If power is the ability to put things right in a person's life, then these good doctors have an endless supply of it.
Pain-management specialists have the power to help people with soul-crushing and career-killing pain so that they might get back on their feet again and work. Or, they can banish the pain at the end of life so folks can float away happily into the great beyond. What life-saving modern surgery would even be possible if it weren't for the medical pain-killing abracadabra of the anesthesiologist?