I wouldn't want that option. When you sleep, you can get away from whatever is troubling you even if it's only for a short while. When you wake up, you can have a fresh start of sorts. Imagine being up and constantly thinking about a big mistake you made at work? If you're up all night, then that mistake will most certainly be in your head but with some sleep, at least it will go away for a bit. Sure, it will still be with you when you wake up but at least you didn't think about it for twenty hours straight.
I have purely obsessional obsessive compulsive disorder. Things are troubling me constantly, and sleep does provide relief. Even so, I'd still rather stay awake 24/7. I'm constantly down on myself, what I can accomplish, what I have accomplished, etc. There'd be so much more time to improve myself if I didn't need sleep. If I want relief, I can always drink :) EDIT: Of course, knowing me I'd probably spend the extra time playing video games and wondering why I'm not reading my library books...