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.
Ah, but there is. Once you go through few interviews you get less anxious about the next one. Which means, that if this is a serious problem for you, and you expect some important interview in the future, then you have to go and interview with some other companies before to gain practice, and may be even get some job offer you'll like more than the one you are hoping for.
The whole point of the parent argument is that there are conscious steps you can take to make whiteboard writing not stressful for you. Just practice for ten hours solving problems on it and it will be as natural as writing on paper.
That's not really practice, it's actual experience.
It's also not guaranteed to improve your skills, it might make it worse if you have a bad experience. When that happens it's easy to make generalisations about the next ones. That's actually somewhat descriptive of where anxiety really comes from, antecipating the unknown.
All practice is merely experience. The only way to practice any skill is to use that skill and get better at it.
It's not the same experience.