The whiteboard is actually not the main problem, it's the other things that often come with whiteboard coding. The main problem is that these type of interviews expect you to master the skill of talking, thinking, and coding simultaneously. The reason given is to "see how you think" but there's no reason this must be in real-time, questions could be asked after allowing the candidate some quiet privacy to work on a solution. To illustrate the main issue, replace the whiteboard with a computer connected to a projector instead. The main issue is still there. A group of engineers silently sitting there, judging, watching every move, and expecting you to keep talking while thinking and coding. This is NOT how programmers work. Most programmers sit down, think about a problem silently, then try out a few quick code snippets to explore the problem, then create a design, and then begin coding.
It would be a huge improvement if companies just gave the candidate a problem, left the room, and came back an hour later. Then they can discuss the solution, ask questions about the code, etc. The key thing is, let them do some quiet alone thinking instead of having to worry about someone watching every move and expecting constant talking.