Mental Clarity - we all know solving problems is one of the great pleasures of climbing. A good night sleep is the biggest factor in have a clear and present mind all day long.
Muscle Recovery - getting a solid 7-9 each night is critical for the lymphatic system to do some serious recovery work. If soreness is affecting your climbing... getting enough sleeping is one method to ensure you're ready to send more routes the next day.
Support the system - as you increase activity and performance...you must also raise your nutrition and recovery game. Otherwise...injury is just a matter of time. Sleeping is the number one recovery method and second place isn't even close.