I like that idea ruff. When I lived in Maryland, I was on the border with DC and the Potomac River and while I wasn't at the station to respond to the river calls, I would hear them go out almost daily in the summer.
When a river rescue call got dispatched, units from Maryland and Virginia (both river banks) and the Park Police helicopter would be dispatched. Often times, these calls were to rescue future Darwin award winners. People who were not qualified or experience white water kayakers/rafters would attempt class 4+ rapids with nasty undertows. Or people would try and free climb near the rapids on slipper rocks. All of which are warned against in numerous signs.
I would have no problem as a citizen paying a nominal fee when entering a park to go towards SAR operations as I know these can be very costly. Just like when I'm planning on traveling out of country, I make sure I have health insurance coverage...preventative and preemptive and hopefully I'll never have to see a SAR team rescuing me