Ah, but the problem with technical interviews isn't the false positives, it's the false negatives -- introverts, people who are inexperienced with whiteboards, people who think it's silly to memorize BFS and DFS when they could look them up, women, people of color.
False positives are way more expensive than false positives. Any filter that is not heavily biased towards false negatives over false positives would likely be terrible for the business goals of interviewing. That is a baseline fact.
I am not sure why you think women and people of color are extra bad at whiteboard problems. In my experience the applicant pool for technical and engineering fields is heavily biased towards white, asian and Indian males, but that happens way before the stage of the whiteboard interview.
