I tend to put proud claims of little sleep in the same category as those of "working" long hours. We've all met people who are at work for long hours, but whether they are actually working, much less producing is another story.
In some cases, it does. My hobby, digital film preservation, requires work that's long, tedious, and relatively-unskilled.
I often clean dirt/dust using temporal fixes in PFClean and having an active well-rested mind doesn't help with this __at_all__, so sleeping an extra four hours won't improve my productivity.
For me, it's not about "get 25% more done". It's more about being able to still spend time with family when I need too and get work done while everyone else is still asleep. It's very much a work life balance tool for me. I can't go weeks on 4 hours though. If I do 4 hours consistently in about 10 days I crash and need a full 8 hours for a day or two.
But over any appreciable length of time, the sleep debt and stress accumulate, the law of diminishing returns kicks in, you run out of steam, and you burn out.
It's like sprinting. You can't sprint a marathon, it isn't possible. Some people can run a marathon faster than others, but no one can run at their top speed for such a long distance. If you try, you will quickly run out of gas and need to rest.
If you're in a game that resembles a 100m dash (like a tech startup or a Wall Street finance or making partner at a white shoe firm) then yes, you can sprint in the hopes of crossing the finish line and getting rich before you burn out. But for most career paths you need to pace yourself.
It certainly could be, but that's not what I take from the examples or experience.
I think this particularly game is more often about perception, not any actual measure or productivity. The banker quote demonstrates it even. It's about "getting respect" not necessarily getting more done.