There are already robots that do that (autobelayers)...

Not really.

Auto belay device can't hold the climber up on the wall, like human belayer can, so that climber can rest and try again.

Auto belay device can't do lead belay.

They're not wide spread but they can do lead belay, I've seen a few videos of it online

https://climbingbusinessjournal.com/could-your-gym-be-gettin...

How do you yell at it to take though