In general, "society" deciding what activities are too dangerous to routinely allow is a really nasty slope. Yes, there's some special insurance offered through private organizations for things like higher altitude mountaineering. But it's not that big a step to rule that any contact sport, for example, should require special insurance. I'm sure the insurance companies wouldn't mind.
I play recreational hockey. All of the rinks around here (and most of the US) require membership to USA Hockey which, among other things, provides some kind of insurance to both the rinks and the players.
One thing which comes to mind is - why should we stop at sports, then? we'll immediately be at the point where smokers, alcoholics, obese people etc. should pay more, after all, their way of life statistically causes higher costs.
(i don't think either of those things should result in higher insurance prices, just continuing the thought.)