Agreed that being woken up is very stressful, but I suspect it's more the stress that's exhausting than the decrease in sleep itself. I'll share a personal anecdote: A few years back I had trouble sleeping, sometimes I'd wake up multiple times and spend 4 hours awake staring at the clock and only sleep 2 or 3. Eventually I figured that as long as I laid in bed and was somewhat relaxed, I could still function the next day, the actual sleep time didn't make that much of a difference. I also didn't drink coffee or take any stimulants to stay awake or anything like that. The problem went away when I moved out of the city after a year or so, some mild allergy I had went away as well. I'm not claiming it's scientific or anything, just sharing my experience.