I'm a shift worker, to a degree.
My previous job was working 12 hour shifts (try working a 7 day week of 12 hour shifts, and complain about lack of sleep then)
Not once was i ever too tired to drive. The only time i have ever needed to pull over for sleep, is when i drove to sydney. The first few hours were killing me, and i had about 4 different 30 minute stops for sleep. then did the last 8 hours in one go. As said, power naps do work.
My job now is all over the place, today i did a 4:30 am start, tomorrow i could be doing a 2:30pm start, but being casual, i have to plan sleep around what i 'think' i'll be working.
I seem to be able to work competently for a shift with minimal sleep, a few weeks ago i finished at my normal job at 11pm, and got called in to cover someone at my old job for a 5am start (12 hour shifts) and was perfectly fine without any red bull. I guess some people just react differently.
The point is the same, you shouldn't be running red lights. As with the other road rules, if your running red lights, how can you be aware of the speed your driving at? Or if your not crossing your lane about to have a head on with someone.