It is possible to work for an extended period with maximum effort.
I know I've been doing it for years at that point. The last time I've properly been off work, for almost two weeks, was at the birth of my daughter nearly four years ago. Then another ten days last summer to attend my best friend's wedding (which, though tremendously enjoyable, involved a lot of traveling and stress.)
However, being at maximum effort doesn't equal doing your best work.
I'm starting to realize that it's quite the opposite. Your maximum effort's value and efficiency level diminish over time as tiredness creeps in.
It is insidious because it's hard to self-assess; it's much easier to assess your effort than its efficiency. And it's easy to fool and pump yourself up thinking that you are working as hard as you can.
Noticeable tiredness is easy to overcome with a short rest.
The problem, though, is that more than a short rest is needed to recover to your most valuable 100%. When you resume work, you don't return to your true best.
That's another argument for considering rest as part of your work. Make it your duty to recover properly.