As you have put it, the white board is convenient for the interviewer, but that is missing the point of the interview which is to assess the candidate.
If you do not find if that difficult, than consider yourself privileged because most people feel differently. Some people cannot speak to a small audience while some love to give presentations.
An interview is already an anxiety-packed situaton where the candidate is under the spotlight. Putting them on the whiteboard solving problems only puts more pressure on and will often lead to sub-performance. Since the interviewer does not follow through when the candidate leaves, they may think that the candidate did his best.
I for one think that there should be an effort to emulate real working conditions and not performatic settings.