Lots of companies do that, fwiw...though I agree that many companies may benefit from doing it more instead of blindly following the "big tech" whiteboard style.

Here's the thing about the whiteboard coding interviews:

A) There's a huge false negative rate. I.E. a lot of good engineers get turned down because of a bad whiteboard exercise.

B) The "big tech" companies know this and do not care. They have people who want to work there lined up out the door. The whiteboard interview is setup to minimize false positives.

C) The above argument can possibly be made in favor of the pair programming/"do what you'll actually be doing" type of interview and with even less false negatives, but frankly those interviews are harder and more time consuming on the interviewer(s). Additionally, the whiteboard panel gives 5-6 people time to meet and speak with the candidate instead of 1-2 which helps to mitigate the effects of any personal biases that might be present.

Tl;Dr - the whiteboard interviews actually work well when you have a giant pool of potentials and only optimize for minimizing false positives.