Chipschap, would you buy a pair of shoes one size too small and wear them to the office just so you can feel "ah, what a relief" when you take them off at the end of the day?

I solve here at CT even when I'm tired but that's just because I'm a chess addict. The value of it as far as solidifying one's skill is indeed debatable.
Doctors in training are often made to endure a grueling series of 36-hour shifts so that they become able to dispense certainly accurate treatment even almost literally "in their sleep". As a patient, one might take comfort knowing that one's physician had gotten their M.D. that way, but I sure wouldn't want to be the med student who had to do it!
Maybe a more productive question for us to ask is, How can we avoid feeling "out of sorts" in the first place? (Or at least minimize the times when we are.) Chess is a physical game requiring physical stamina. When I'm sharp and "in the zone", it feels like no problem is unbreakable. When I'm foggy though, no amount of trying or concentrating can avoid missing seemingly even the most obvious things like checks and captures. So I try to eat right, sleep right, and stay positive in the face of adversity.
(2 cents from someone who hasn't played a tourney in years)