Is there any more bias than the interviewer picking the question to begin with?
By letting the interviewee pick, we're letting them decide which of their "superpowers" to show off. If they can explain why they chose to do something the way they're doing it, and show they understand the tradeoffs, that's good enough for me.
There's a benefit to having a standard question that you can grade independently, you can uncover your own teams biases by having two people evaluate a candidate. One who met them, one who didn't. It can avoid interviewer bias with decision.
It sounds like you're putting that system of bias under the rug.