It's a whole separate skill to be able to code with an audience, let alone an audience who is judging you. I could forgive a non-technical interviewer not knowing this but surely someone who is a dev themselves understands the very real performance anxiety. It's bonkers why we do this to people— the best I've seen is the in person talks about their experience, architecture, problems they've encountered and how they solved them and then either code samples from their public code if they have some or a short take-home assignment if they don't.
They could cheat on the take-home but it isn't meant to be difficult and you hopefully figured out at the in-person that they're someone who wouldn't need to bother cheating.
I can't code with somebody looking over my shoulder. I need to relax and think about the task. They expect me to code while being judged by one or more strangers, against the clock, with high stakes involved. If that was the actual job I would not apply for it.
A good analogy I’ve been told is the NFL combine. Vertical jump, straight-line speed, and bench press performances are probably moderately correlated with on-field performance, but the best test of playing the game is playing the game.
I more understand the emphasis on leetcode problems for juniors but a timed session without an observer (perhaps with browser tracking) to solve those problems makes a lot more sense than bringing in the anxiety of the observer, as you’ve noted. It sucks having to spend mental energy wondering how your problem-solving looks to whoever’s watching and seems actively detrimental to assessing talent for an IC role.
It's almost impossible for me to do any serious work or problem solving in an interview situation due to anxiety and stress-my mind simple does not work the same way as it does when relaxed and in flow.