If they can afford to go down there, their families can pay from the estate. Why should I have to pay through my taxes for something like that?
You shouldn't. Of course, there would have to be some limits or else the government would be expected to pay the cost of every mishap and act of nature that anyone experiences.
But when the undertaking is experimental or in the daredevil category, and it has not been insured by the promoters against any failure, there's no reason for the government to have to pick up the tab. It's quite enough that the government does the rescue work without also sticking the taxpayers with the bill.