It's not like it takes very long to be able to ride again, even a minute will make a huge difference, if you're in pretty good cardiovascular shape. Plus it feels good on the feet and undercarriage to give it a tiny break.
I've noticed, riding like in a Century or whatever, when you see the same riders over and over again, you always beat the "walkers" up the hill/mountain if you stop, rest, ride again. It's more efficient.
Now on trails, no way, if I have to stop, it's all over for that hill. I'm walking.
Nanci
***********
"...I'm like the cycling version of the guy in Flowers for Algernon." Mike Magnuson