If there were no friction you wouldn't be able to stand on a hill without sliding down it, let alone climb a rock face.
More specifically...
In any technical rock climbing you are required to use your feet and fingers to balance, hold on, etc. This often requires a little ingenuity, and always requires a good deal of friction since you often are standing on ledges and nubs smaller than your thumb. Some moves may even require you to push off of a smooth rock and just hope that your climbing shoes are sticky enough to give you the boost you need.
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