It depends. Sometimes the best time to speed is when something else is already accelerating you.

https://en.wikipedia.org/wiki/Oberth_effect

I don't think this is one of those cases though. See Terry Tao's take on a similar problem about when to tie your shoelace: https://terrytao.wordpress.com/2008/12/09/an-airport-inspire...

I believe that is specific to how rocket engines work. I once thought it applied to bicycles, but that must be some other phenomenon...

it certainly applies to bicycles in orbit.

Sure, but that's a tiny fraction of all bicycles, probably less than 1%.

* According to current knowledge.

Depends what you're optimizing for- energy or time.

Some people, the goal is to expend the least energy. For some, it's to accomplish more things faster. This is true in realms outside of escalators, and in fact in all of life.

Sure, but "I usually camp at the bottom, waiting for the crowd to disperse, then grab the powerup and use it efficiently." optimizes for neither.

There are a whole host of other things that are potential optimizations, like not being pushed around in the crowd.

Agreed. That does seem silly.