Most startups _do_, don't they? That was definitely the case at the company I worked at over the summer. My normal hours were something like noon-2am... all-nighters weren't too uncommon either. Sometimes you're too tired to be productive, but other times it seems you're just tired enough to really nail it down... sort of like Ballmer Peak (http://xkcd.com/323/)
I've found there's set of tasks, particullary administration of *nix boxes, that are too boring to be made in day hours, so I schedule them to the night.
On the other hand, I don't think that any startup can waste their founders' wake up hours. They're simply too effective to be spent on crappy things.
What's interesting, most of the time management techniques tend to overlook this aspect.
As co's get bigger they tend to enforce stricter day schedules, killing any potential for late night hackfests and flexibility to run errands, etc.