FWIW I think the primary reason they want this is so that if they find a kayak or paddleboard somewhere, the authorities need to know if they should start looking for a person and/or a body. By having the phone number they can call it and say "Hey, we found your kayak on the Platte River, are you OK?"

Lets them know if they have to start searching and also keeps them from expending search and rescue resources unnecessarily.