They are extremely useful to filter out candidates that simply cannot program, and who won't be able to no matter how much mentoring time you 'invest' in them. I've heard about interviews for senior engineers that were totally derailed by a simple FizzBuzz. I like wordcount (the wc *nix command) as a warmup/screening question simply because either: The candidate comes up with an algorithm for it and test cases OR starts counting whitespace and derails the implementation with a cascade of if-else for every new test cases that breaks the previous implementation (I've seen if-else to check for the n cases I suggested...).

But honestly I feel there is so much cargo-culting for coding interview. Especially if you ask for compliable code of well known (as described by a textbook) algorithms you ultimately assess rote memorizations skills and not engineering.

Convex Hull doesn't sound so bad to be honest. If I was using this question I would expect someone to be able to come up with the gift wrapping algorithm with maybe a little bit of help. What, as an interviewer, would really want to see is if the candidate can come up with test cases and a way to test whether his solution is actually a convex hull and then try to break down the problem and come up with an algorithm. I sure wouldn't expect to be able to type what's on the board and for it to compile right away (it's a board, not an IDE!) but I expect the candidate to be able to walk me through the code and run it line by line through some test cases.