Comment by CydeWeys

For what it's worth, being able to run programs "in your head" is a very common skill required of Computer Science undergraduate programs, where you're required to write programs of medium length on paper during exams. You should be able to write out, follow along with, and reason about the correctness of a program that can fit on a single piece of paper without having to run it. Programming hyper-iteratively is not really a good thing, especially not in environments where rebuilds or test runs can potentially take hours.

Another reason not to have candidates run the code is that they tend to get really hung up with debugging trivial errors. I've conducted a fair number of interviews either way, and the white board interviews were usually more pleasant experiences for all parties than the interviews where the interviewee was expected to execute the correct solution in front of me. The latter almost requires giving them some kind of web or library API access, which then just makes the distractions worse. I don't want someone worrying about what the exact name of a sort function is; that's not what I'm trying to evaluate in an interview.