I think your thesis holds, but I don't think it's clear that your example does (though it certainly still could). Depending on just how much chance of accident goes up over time, and just how great a "productivity" hit we apply for an accident, it is absolutely the case that your productivity falls at some point and it's conceivably the case that it's before 12 (or even 8) hours - though for all I know it's at 15.

I'm sure the fatigue that sets in after (say) 15 hours would be a serious factor in accident risk. I mean truckers are required to stay under a certain work day/week and get enough sleep for safety reasons. Sure if they drove 24 hours straight they would get there faster and in theory be more productive but there are serious safety concerns both with the driver and with the truck (less time for maintenance or inspection)

agreed. My typical pattern on weekend nights is to sleep for 10 hours (yes 10 hours), do what I need to during the day for about two hours, and then get on the road, I'm usually taking anywhere from 1-2 hours of break doing other things that involve momevent (e.g. exercise, social dancing) within that 12 hours, as well, depending on availability.

During the week (when i work more protracted hours) I'm sleeping about 8 hours at least, and I'm also not beholden to an alarm, so I get as much sleep as my body needs. I think I'm probably one of the most well rested people I know, despite pulling twelve hour 'shifts' three days a week.

Obviously I'm more tired after I do the 12 hour shifts than during the week, but I haven't felt so tired that I was at risk of falling asleep on the road (which happened from time to time when I was in grad school).

Yes, also relevant might be the difference between what is safe as a one-off (maybe you really can drive 20 hours safely in a day, if you're well rested beforehand) and what you can do sustainably day after day.

In principle, this is stuff that insurance companies should be on top of...