I always find it odd when I see doctors saying stuff like "I have a duty of care, so I work 24/7 if I need to." I dunno about doctors, but after 12 hours of wor

I always find it odd when I see doctors saying stuff like "I have a duty of care, so I work 24/7 if I need to." I dunno about doctors, but after 12 hours of work my mind is toast, and I wouldn't trust myself to operate a toaster. I find it really hard to imagine the same thing does not apply to them. Is an absent doctor really worse than an exhausted one? I mean, there's obvious situations in which this is the case, but is it true on average? If someone arrives at the hospital and dies because there is no doctor available, only for that doctor to go and save 3 people that might have otherwise died the next day because they're not exhausted, should we make that tradeoff?