You go through all the pomp and circumstance like it actually mattered, even though the majority of the people running around know it doesn't.

Perhaps it is a politically-correct version of this: https://en.wikipedia.org/wiki/Chinese_fire_drill which includes the substitution of mere activity (all hands on deck & running around) in place of the desired results.

The vast majority of business firedrills are arbitrarily caused by someone wanting a deadline met for no particular reason.

Everyone does crunch time not because there is actually a pressing emergency, but because the company wishes to extract additional effort for no additional pay.

Hm, ok. That's not been my experience. For example, I have definitely heard it used in Operations contexts to describe broken shit that needs fixing now -- things that are real problems and not drills. "Drill" to me implies preparation for an event in the future like a test or an emergency.

I imagine it's due to the superficial similarities, i.e. a bunch of people running around not really knowing what they should be doing, but in a big hurry.