Lots of great points made in this thread. Here's pretty much the same in some stricter word-packaging, because some people need that and maybe you're one of them. I definitely am. (; If you're not, just skip this post.
Being tired is your body telling you that its batteries are low. You know how your phone, laptop, or electric toothbrush gets really sluggish at low battery levels? Or how any battery-powered machine gets really slow and frankly kinda useless with an almost empty battery? It's exactly the same thing with your body. Let's be honest: How great do you think that the work you do while being sleep-deprived is? Spoiler: Not good.
There's been a lot of research into sleep, tiredness, work efficiency, and injury rates. Driving tired is just as dangerous as driving drunk. Sleep deprivation leads to both physical and mental illnesses (and how productive will you be then? Another spoiler: Not at all.). Workplace injuries skyrocket with overworked and tired personnel.
And what about the country of ganbari, work-till-midnight, work-till-you're-sick-and-then-some-more, Japan? Take this from a Japanologist: The companies promoting this work/life-style aren't more efficient. We're still humans, not machines. A tired employee is not an efficient employee. The employees in those companies just end up sitting there, thinking "I'm so tired", "I want to sleep", "I don't feel like doing this but I should", instead of just doing those things... Which they could, had they been allowed to sleep.
TL;DR: If you want to get shit done, not sleeping is the most idiotic thing you could possibly do.
Oh and another thing: Just like there's a minimum of sleep necessary to function, past a certain number of hours' sleep you don't feel more rested anymore, but you get stuck feeling sluggish all the time instead. Where this point is varies a lot between individuals, and is also dependent on age and lifestyle, but the breaking point seems to be around 8-9h for many. Furthermore, sleeping at the same time of day each day helps your body stay alert during the day and being ready to sleep at night. Therefore, pulling irregular all-nighters and then crashing in the following days is monumentally unhelpful.
In other words, sleep efficiently => work efficiently => feel happier.