Many people believe that it is completely unreasonable to ask an interviewee to write code on a whiteboard at all. I disagree with such an absolute position. I do think it can be a reasonable thing to do, but only if you are asking the interviewee to code something really simple.

When I say simple, I mean really simple, like FizzBuzz simple.

There are interesting questions you can ask that are really simple which are not FizzBuzz. I've used the Fisher-Yates shuffle algorithm and more recently Selection Sort. I should stress in both of these cases that I carefully explained the algorithm before asking the interviewee to code it up. Even though these algorithms are quite simple, I do not expect the interviewee to have memorized them.

I do expect someone who is a professional software engineer to understand the algorithms after a decent explanation and then write code which will implement them.

I also don't necessarily expect the interviewee to get the code exactly right. I just expect them to demonstrate that they could write correct code given enough time and access to an actual computer to test the code on.