I've definitely seen smooth talkers with great resumes get through any other filter, but I've never seen a false positive with the technical interview.
I've seen way more than a few false positives from tech interviews, along with tremendous amounts of false negatives: People with backgrounds of being transformative to teams and organizations that just couldn't look good enough while solving random algorithm problems to save their lives.
It's just hard to see the kinds of things a company misses when they keep insisting in asking people about graph algorithms and implementing red black trees, because those same companies just never get to see the kind of people that you get when you do things differently.
I currently work for a company that does relatively traditional tech interviews and does 95% of sourcing from big schools and ver well known tech companies. I fail to see a major difference between my coworkers here vs my coworkers at places where your average dev went to a midwest state school and was never asked an algorithm question during interview.
I guess you could counter that you need to have a 10x longer technical interview that covers all these aspects, but a long interview process is going to filter out all the candidates who are good enough not to have to put up with one.
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.
Any interview/test/discussion without overwhelming objectivity will be subjective by nature and therefore subject to emotional bias.