Physical arguments aside, I would have to
disagree with this theory. And I'll tell you why!
Sleep is pretty much the only time when a human can dream. What's that? What about daydreams? Well, from the definition, a dream occurs when you are sleeping. A daydream is defined as "a pleasant visionary that is usually a wishful creation of the imagination." So that takes care of that.
It's a common feeling among psycologists and psychiatrists that dreams help one to relieve stress and pent-up emotions from things that might have happened during the day. I guess its like that time when I ran over my dog with that riding lawnmower on my birthday. That night I had a dream about...running over my dog with a riding lawnmower on my birthday. Weird. Just kidding.
But seriously, one theory is that dreams are fabricated by the mind as a way for people to subconsciously deal with stressful of emotional issues that they may be dealing with.
For example, lets say that you get fired. That night you go to bed, have a dream about killing your boss with an icepick INSTEAD of staying up all night planning on how to get back at those bleeps with a pipe bomb. You wake up the next morning feeling refreshed, having gotten rid of that stressful hostility and go out looking for a new, better job!
Of course, the next guy to get fired just might not go to bed right away. I think they call that the "postal factor". I can see that you understand. :)
Maybe, if you have no stress, i.e. if you're an old monk in China who practices Yoga everyday to relieve the stress, you could very well go without sleep indefinately. Very interesting indeed.
But I doubt you're a Chinese monk, so go get some sleep!!