Please tell me you guys do capacity planning with more than just vague numbers you pull out of your ass, a whiteboard, and some guy staring at you making subjective judgments of the number you come up with.
Yes, but we don't expect someone to use actual numbers in response to a hypothetical question in an interview. The question is intended to see if you could figure out which numbers you'd really need to figure out the right estimate.
Often, the specific result of an estimate is less interesting than the user's understanding of what drives that estimate, because it determines if they understand the levers they can pull to change the outcome in the real world.
You don't want to ask the actual question about the specific application, because it gives a strong advantage to a candidate who has worked on that very specific situation in the past (and they may be able to sneak through just by regurgitating from memory.) It's better to have a scenario they're unlikely to have seen previously. As an interviewer, I'm not interested in your ability to remember solutions you received from others, I want to know how you deal with a problem you haven't seen before.
Sometimes folks call these "puzzlers" but I think they're unfairly lumped in with true "puzzlers" - crap like "why is a manhole round" where there's a right answer that depends on either experience or some specific insight. A question where you're asking a candidate to walk through their thought process on a hypothetical (but reasonable) situation isn't "puzzling" unless you just can't handle the question.
Well that was a little condescending. If you think it's vitally important to screen people for their ability to solve Fermi problems, it's no skin off my back. I was just trying to have a conversation.