I think one of the things that might help is understanding how small the cost of S&R is compared to the income generated by the outdoor recreation industry.

Sure the cost of one rescue mission for one individual looks big, but you have thousands of people hiking, camping, hunting, 4x4ing and every other activity under the sun.
Those people are all paying out money to equipment dealers, lodges, restaurants, resorts and to governments for licenses and permits.

I think rescuing people who happen to do foolish things should just be counted as part of the cost of doing business.
If you don't do that you really risk hurting the tourism sector of your economy.

In the last New Hampshire State $10.4 billion two-year budget, they refused to approve $100 thousand in funding for Fish and Game's SAR services, expecting it to be paid for out of the fishing and hunting license fees.

Now note that the outdoor recreation industry in New Hampshire alone:
Supports 53,000 jobs across New Hampshire
• Generates $261 million in annual state tax revenue
• Produces nearly $4 billion annually in retail sales and services across New
Hampshire – accounting for 7.8% of gross state product.

And that they were too cheap in that State to come up with a mere $50 thousand a year to balance the funding for SAR services.

Consider also that deliberately underfunding public services is a standard ploy in campaigns to privatize those services.