If this became popular, wouldn't people start rehearsing for it like they do Leetcode interviews, and it would be become another performance that people focus on and optimize for, rather than on the skills for the job?

Rehearsing how to teach something is not a bad thing.

And I'm sure you're going to get different questions about different aspects of the things you're trying to teach from different interviewers. The wonderful thing about this is that it models trying to teach a concept to a fellow coworker. How you handle the questions during the teaching time says a lot about the candidate.

But would this train people to teach well?

Or would it train people to choose topics very carefully, such that a little teaching skill goes a long way?

It's not like the interviewer getting a lesson in tuning a harmonica is going to bust out a harmonica and start putting his newfound knowledge to work, or revisit the subject in 6 months to see if he's retained the knowledge, or bring in a panel of harmonica tuning experts to check there weren't any major gaps or mistakes in the lesson.

I think the lesson to be learned from the parent comment is to put candidates at ease and let them express their interests. I think it doesn't matter if you chose to use "teach me something" specifically. However, it does matter how to try to be accommodating towards the candidate either by asking about their hobbies, some recent news any fond memory/project etc.

I forgot to include something important in my initial comment. In my introductory email, I explained that the "teach me" segment is completely optional.

If someone didn't want to do it, that's fine and wouldn't be held against them. In practice, I think one person out of 20 chose not to do it.

And if they weren't a great teacher, that was fine too!

The purpose of the segment is to give the candidate a chance, if they want, to shine at something they are interested in, and help put them at ease by letting them start out being the expert.

Of course. Campbell's law[1] applies.

[1] https://en.wikipedia.org/wiki/Campbell%27s_law

I think the point is to remove the adversarial aspect and therefore see how they react when not under pressure. I wouldn't be surprised if OP does warn their candidates about it.

You have it exactly right. I always told the candidate in my introductory email that the segment is optional and I like to learn all varieties of new things and they should feel free to pick any topic they want.

And then when they were teaching me, I made sure to pay attention, ask questions about anything I didn't understand - not to judge their teaching skills but to show I was interested and listening.