You're one unfortunate motor control fuckup away from killing yourself pretty much always. Most animals are good at not killing themselves and humans are decent at climbing to boot.

Yeah, if you fall you might hurt yourself, but when you're paying attention to what you're doing you're likely less at risk than when you absent-minded walk down some stairs.

We spent probably hundreds of hours climbing all manner of tall playground structures as children, and I cannot recall anyone ever falling. I do remember some instances of people tripping and falling down a flight of stairs though...