... will typically code better with a keyboard and
editor than someone who relies on the keyboard
and editor to be able to code
The whiteboard sucks for problems for which you either don't know the solution, or for which you know the solution intuitively, but can't reproduce it line by line in successive order. In such cases people go back and forth, adding new functionality or correcting the existing lines to fit a new condition ... and this happens a lot for recursive algorithms. For instance I cannot reproduce the in-place QuickSort line by line, but I can work it out by evolving it from the basic idea, a process that takes a couple of minutes and a lot of corrections.
So you're basically encouraging people that rote-learn solutions and that line above is bullshit.
Leave room between the lines so you can add stuff. Mark it up as you evolve it. If you need to, you can rewrite the clean version on another part of the board. Better yet is if you can figure it out in your head before you start writing, becaus that will definitely make you a better coder.