I'm one of those guilty parties who frequently ask this type of question in interviews. (For the record, I also ask similar questions about their "favorite project.") The reason I ask is that it's something we frequently do around here. We get design engineers from all sides of an interface, someone from systems engineering, someone from test, and someone with some knowledge of customer use cases for the feature. We stand around a whiteboard and say, "Okay, how are we going to build this thing?" Often you know very little about the new feature at that point and are only there because of your expertise in your part of the system, but you are still expected to contribute productively. It's not just a hypothetical academic exercise.
As far as what kind of answers I expect, take for example, designing a system to download new firmware from a server, through 20 embedded line cards in a central office to upgrade 5000 set top boxes in the field at once. Assume there is very little spare capacity on the link between the server and the line cards.
Um, I would probably use ethernet or something like that.
How large an image are we talking about? [Around 7 MB.] Well, you'd want to make sure service wasn't affected during the download. You'd need extra flash or RAM to store two images at once. You'd probably want to cache the image on your line cards in order to avoid downloading the same image over and over from the server. Being embedded, your line cards probably have limited CPU themselves, so you might need to serialize the downloads in order to leave enough capacity for service. You'd want some way to verify the image was good and fall back to the old version if it didn't work. You'd need some way to retry a few times and report errors to a human if the upgrade fails. If you have different brands of set top boxes, you'd need some kind of way to identify which image you need to send it.
Those are almost word for word transcriptions of two different candidates. Most candidates are somewhere in between, but usually get there in the end with a little prompting, which is perfectly okay. We're not looking for the next Einstein here, just an indication that you can actually reason intelligently about the kinds of problems we work on every day.