I was under the impression that this question in particular was extremely common, and that most candidates already have heard of the solution. Because of this, I really hate this kind of question because you're getting an incredibly skewed view of the applicant's problem-solving skills.
On the other hand, while design questions are important, there are other important qualities of a candidate that aren't best assessed by knowing how her or she would design a system (such as coding/problem solving/logic skills).
I think the main point is interviewers should stop being lazy and come up with their own unique questions. For example, when I was interviewing at companies after college, I got the BST least common ancestor question at least 3 times. I'm sure the 3rd company had a much better impression of me than the first, even though I didn't get any better at problem solving.
A simple question I sometimes ask is "through a football game, you can score (for simplicity's sake) some combination of touchdowns (7 points) and field goals (3 points). Write a function that takes a final score and outputs the number of possible ways a team could've reached that score."
OP, best of luck on the rest of the interview process!
OP, best of luck on the rest of the interview process!