But communication on-the-fly, on-your-feet, in a high pressure environment, which is what a whiteboard test is, is not most communication.
Most communication gets thought about, drafted, revised, critiqued, socialized, ahead of distribution.
If your whiteboarding comes after hours or days of consideration and review, that sounds like a great way to vet good communicators. Otherwise, aren't you optimizing only for speed? If someone cracks a joke in the moment, they're a wit; but we only pay money to and call comedians those who worked on it for a while.