For the speeds involved, helmets result in more head injuries. Cases where your head would have hit nothing, the helmet catches it - a bigger target and more torque.
Yup, I'd say an impact from traveling 15-20 mph would mostly be worse without a helmet. There's no credible argument for a fall like the pool rider.
I've known it to happen. I usually go flat on my back on solid ice a couple of times a winter. Neck muscle strength, range of motion, something keeps me from bouncing my head off the ice.Sister in law had a coworker slip on the ice, fell backwards, hit head, died.