I disagree. Unless the candidate desperately needs this job, he/she can walk away. The candidate is free to consider "company won't bother to answer my questions at the point when they have most reason to be nice to me" as a bad signal.
> I am specially referring to companies that don't really have to care about your feelings towards their interviews
"This company doesn't have to care about my feelings because they are huge and have lots of applicants and a giant incessant interview machine chugging through them efficiently" is certainly something I'd consider in whether I want to work for them, because it tells me I'd be a cog in a machine. (And if enough people consider that, perhaps they will have to care.)
To the parent question: I wouldn't ask a whiteboard question exactly, but I would certainly ask some questions about existing architecture and rationale so I have an idea what I may be working on.