Grenades are mostly used at closer and more hectic ranges, so it's often much faster to just throw it instead of having to prepare some sort of implement to increase range.

Hand grenades, sure. There's a reason we have grenade launchers though. They can fire several hundred meters. With that said, is there really a need for a sling? I could see gorilla forces making good use of them, as they'd be silent, cheap, portable, and a lot easier to hide. Conventional forces have no need though because either you're close enough for a hand grenade (there are different types, some are thrown further and some not), or you have grenade launchers available to hit the further away.