Evolutionary pressure

I have been thinking, what could really be the evolutionary pressure to develop a mechanism that whenever one feels like "I have something very important tomorrow, I need to get a good nights sleep" or "I won't have many hours to sleep tonight, I better go to sleep asap". And instead of falling asleep, you lay and twist and turn, think about every stupid thing you don't want to think about (including the necessary "I really need to fall asleep now!!").

I can't see how even hunters would have benefited from that. Maybe if they were worried their area of current habitation was full of predators, so they didn't fall so deep asleep. But still, they would have fallen asleep! Otherwise the predators would have gotten to them sooner or later, when they would fall asleep on a stone during the hunting. Or also fall asleep next to the evening fire, putting their hair on fire or something. That wouldn't be too good either, right?

I am really into evolution at the moment, sorry for that. And also, apparently, not getting any sleep tonight.