I always try my best to hang on to a rein. I'm not always able to, but I try. In the area that I ride, there is a fairly major highway in every direction plus all of the pasture fences in this entire area are barbed wire so a horse running loose is a recipe for disaster any way you look at it.
My way of thinking is, if a horse gets me off, it's because they were doing something that is unacceptable (bucking, huge spook into a bolt, etc) so I am not terribly concerned about them hitting the bit when they try to run away. It might make them think twice about doing whatever they did again. Not only that, but it also helps a young horse to learn that running away after your rider falls is not acceptable. I work on getting them to stop when I step out of the saddle anyway, but hanging on to a rein will enforce that in a moment of panic.
Not only that, but if your foot were to get stuck in the stirrup and you still had ahold of one rein, you might be able to keep the horse somewhat under control in a circle instead of having them just run away full tilt and drag you to death.
Of course, it is important to recognize when hanging onto a rein will put your own life in danger and learn to let go then, but many times, hanging on doesn't hold any more risk for yourself than letting go.