A throw rope is a key piece of paddling gear right behind the initial “five.”
But like any rescue equipment, use a little common sense! Have it inside your kayak. Secure it around your waist. You chose. But be advised that there should never ever be something attached to the outside of your kayak. It sets up a potentially dangerous situation if the throwbag was to come unpacked while still attached to your boat.
There are varying opinions on “safety procedures” on the river. Think through all opinions and decide what is best for you. A resource to start with can be a set of three articles that ERA staff authored.
And remember: if you own a throw rope and your paddling buddy does not, your buddy will be good to go if/when he needs a rope. But you will not.