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.
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.
This makes a lot of sense to me, and might explain what's going on with the puzzling uses of "fire drill" I've witnessed in recent years. I almost want to say that there's been a shift in jargon going on, because I feel like I hear people talk about fighting fires at work less often than I used to say, a decade ago.
To the degree that it's systematic, I'd say it's probably a perjoration as people became uncomfortable talking about fighting in the workplace (or whatever).