I was speaking of sports specific insurance which is designed to mitigate the risks associated with specific sports. Diving injuries are often not covered by medical insurance, so specialized insurance is necessary unless the diver has a large enough bank roll to cover treatment in a hyperbaric chamber (the most commonly required emergency treatment for divers. Evacuation coverage is part of the coverage, but it is certainly not all of what is included. Decent diving specific coverage is available relatively cheaply (~$130 a year) to cover the kinds of risks I identified which are associated with diving, and to fill the gaps deliberately created around the edges of standard insurance policies.
http://www.diversalertnetwork.org/insurance/plans.asp It would be silly to purchase dive insurance if I were a mountain climber. I am not a mountain climber - I do not specifically know what insurance is available to mediate the risks associated with mountain climbing, but sports specific insurance is available for most sports and I expect mountain climbing is no exception. If I engaged in that sport, I would certainly research what insurance was available and would treat it as part of the cost of engaging in that particular recreational activity.
As to where the cutoff is, as I suggested earlier, if the activity is routinely listed as a high risk activity on life insurance applications (a sample list here:
http://www.forsalebyowner.com/term-life-insurance-tips.php), then it is probably more dangerous than the rest of society ought to be expected to bear the cost for. None of the activities you suggested are on that list except for scuba diving. Mountain climbing and scuba diving are, incidentally, on that list and is on every similar list I have seen.
As noted, it is my choice to dive. I accepted the significantly higher than average risks associated with diving when I took up the sport. Most folks I have spoken with who engage in similarly risky activities have a similar philosophy. I can choose to maintain enough money in savings to pay the bills for those risks should they materialize, or I can purchase insurance to cover them. but I would not presume to pass the costs on to you in the form of additional taxes.