What a can of worms.

Call for no good reason, you get a bill.
Call for a good reason, but the reason you are calling for is your own fault thru being stupid (climbing without gear in winter let's say) and you get a bill.
Call for a good reason, and due to no fault of your own, you get rescued and no bill.

But who decides who gets a bill? This puts many people right on the edge - and they probably won't call and will die without rescue, leading to screaming meemee mobs of half informed people at the gate with pitchforks and torches (ok, maybe not pitchforks).

I know there is insurance out there. But the same morons who drive without insurance are the same people probably needing rescue from wilderness situations.

Makes your head hurt.

I say rescue everyone, then investigate why they needed rescue. If it is because they were more stupid than not, charge em.