While a good idea in theory, I wonder if there could be legal issues of being forced to pay for a rescue that you did not ask for. I wonder if there should be (or is) some sort of waiver form that says “Yes, I authorize rescue efforts” or “No, leave my dumb butt out there (with the appropriate release of liability legalese included)”.
When I worked for the US Forest Service in the White Mountains of NH during the 70's and 80's I went on a number of rescues. Sad to say, IMHO, many of the local entities such as Fish and Game, US Forest Service, Appalachian Mountain Club, and a host of others treated it as a lark. They would drop everying and drive to the location in droves 'cause rescues are fun and work isn't.
Plus you get overtime.
To just take an injured hiker down a couple miles of trail about 50+ people from various agencies would show up, most milling about with no clear objective, some jockeying for position in order to have the honors of carrying the litter the last few feet so that the news photographers would get a picture of their "heroic" efforts in saving a mountaineer.
If I were that "mountaineer" I'd be mighty angry footing a huge unecessarily inflated bill when it was my tax dollars that funded these jobs in the first place.
Think of it this way - if you were injured at home and 27 ambulances showed up would you be willing to pay for all of them when only one was necessary?