All of my players know that as soon as a fight starts when they are climbing, they are deeply into "rule of cool" territory. They can be darn sure that they will be making rolls or fall and that they will be given all sorts of ridiculous ways to stop other people falling.
Our last fight that involved climbing also involved people grappling then riding harpies through the use of athletics/acrobatics/intimidate. People were pushing off the cliff diving down with a rope to save falling companions and the Eladrin even jumped off to grapple somebody that was being carried away by a harpy then used "Fey Wayfarer" to teleport them both safely to a cliff edge. To top it off, the Artificer who uses a superior crossbow spent a turn rigging up his super-light wire to a barbed bolt. He then shot a friendly NPC through the leg as the harpy was carrying him away, then reeled him in like a fish.
So yeah, rules are a mere suggestion when there is opportunity to swash and buckle. To the posters above saying to use common sense, I say pheeewy

Common sense is over rated.