I am a big fan of "tag" lines for cats. For me they serve both safety and convenience functions.
More often than not I am in my cat by myself so self-rescue is the name of the game. Tag lines provide multiple extended grab points should I find myself out of the boat. The same holds true if I am chasing down a swimmer. They can also sometimes provide a sufficient grab point for assisting with helping to get a stuck boat unstuck without having to pull out a rope.
As mentioned previously, they are convenient for holding on while on shore, landing by myself or with assistance and they provide an option for a quick tie off to another boat.
Mine are 6' long made out of flat webbing with a loop at one end for easy on off (think loop strap but without the second part with a buckle). Jan at Stitches N Stuff made these for me since I wanted a specific length and didn't need the extra strap with the buckle.
In my opinion, tag lines do not pose a hazard. I always use them regardless of the river and have never had them catch on anything. Maybe there is a chance of this, but for me the positives far outweigh any potential negatives.
Goofy? I don't know about that. I do know they sure come in handy.