Here's another disadvantage of whiteboard coding: it's inaccessible to blind people, and impractical (even more than usual) for people with only a little vision (like me). Such candidates will need to do the coding on a computer, so one might as well make that the default, as the OP recommends, and eliminate one variable and a possible source of bias. Of course, once a blind or low-vision programmer stays at a given company long enough, they'll probably be on the other side of the interview at some point. So for consistency among a team of interviewers, I imagine it would be best if all of them have their candidates do coding problems on a computer, not just one of them.
I'm curious about why whiteboard coding is still a thing in the first place. Is it a matter of convenience or cost? If so, surely that equation has changed now that we have ubiquitous, cheap, portable computers. Or do some interviewers really think that it's good to deny a candidate access to a real computer while solving a coding problem during the interview?