I have done this before, with some success - however, I think you might be missing the point slightly of a white-board interview. Yes, one purpose is to assess your coding ability, which you're right to say a short project could achieve.

Another is to assess your ability to brainstorm and talk people through your ideas. If it was about coding ability alone you wouldn't need the whiteboard - you could just be sat in front of a computer. I can think of several people I've interviewed who have produced very good code, but have lacked the social skills required to integrate with a large team - even working remotely. So I don't think the solution is quite as easy as you think.