There was a famous case in 2017 where a surgeon was violently removed from an overbooked United Express airliner. He had refused to leave voluntarily, as doing so would have meant not seeing his patients the next day. [0] I'm not sure this strictly counts as travelling for work, but the points remains.
Plenty of people fly abroad for medical care. [1]
Over 2,000 flights were cancelled in this incident. Over 300,000 would-be passengers were affected. [2] It's implausible that nobody's medical care was affected.
The US has a bunch of highly paid medics who fly every week or in some cases every day because they work somewhere with enough population to justify their practice but they choose to live somewhere hundreds of miles away, and at their income it's actually practical to have a small private jet. It's probably only a small minority of the most highly paid (so e.g. cosmetic surgeons) where this makes sense but it's more than a handful of people.
Likewise because it's big and a lot of it is empty the US does more medical flights than a country like the UK, if a Wyoming multi-millionaire needs urgent treatment in a Californian hospital you're not going to load him into a truck and drive there, you use a plane. This is relatively high risk commercial air travel, it's not quite as dangerous as most GA but there's some get-there-itis because you don't want to abort the flight and let down your patient, and you're often flying one-off journeys whereas the people doing scheduled passenger travel it's like a bus, same route, every time, regular as clockwork, and if things go wrong you just scratch the flight and no harm, no foul.
