That $3 million NPS budget (which also includes National Forest Service under Dept. Of Interior) was about 00.13 percent of the overall budget.
Metrics collected in Yosemite from 2000-2004 indicate hikers "cost" three times more than climbers in SAR (and that's at Yosemite!!).
So if we assume the entire budget was only hikers and climbers (which it isn't), that would be about $750K for the entire annual SAR budget used for climbing incidents.
That's less than 1 cent per taxpayer. One penny. To be more precise, 0.75 cents per year.
Your assuption of equal costs is invalid. The top 1% of taxpayers pay 38% of the taxes the top 10% pay 68% of the taxes. SO if you're assuming 100,000,000 taxpayers then the top 1% pay $.28 cents, not $.0075 All of which is irrelevant anyway -
What is relevant is that people should be charged for the taxpayer provided services and by all means charge the hikers too. Mountain climbing is inherently risky, and if you want to do it, then accept the consequences including paying for an SAR efforts. You don't get free stamps at the post office, why get free government sponsored SAR activites (and if volunteers want to do this then more power to them).