At least then it wouldn't be purely artificial. I'm not surprised at all that there are so many people "bad" at technical interviews when they are fundamentally designed to leave you a fish out of water. Nobody likes to flounder, but some people it shakes much more than others.
But I wouldn't think for a second those people would be incapable of being good team members or productive coders. You just let them stay in their comfort zone and approach uncertainty in the ways they are comfortable with. They will know the best way they can approach solving a problem, and if you were testing for that instead in these interviews, they wouldn't be so harmful to participation in tech by "minorities" such as women or people of color.
Wouldn't it be nice to be able to use references / existing implementations while at the board being watched and timed.