As soon as SAR involves a helicopter, I remember hearing you're looking at a hefty bill in many places, even if the SAR teams themselves don't charge anything. (Not sure why/how that is the case – maybe the helicopter is often operated by a for-profit company, essentially taking the SAR crew as passenger?)
As someone who’s been rescued via helicopter, I can state at least in my case there wasn’t a large bill. The only thing I was charged for was the out of network ER visit.
Yeah, I'd imagine the helicopter is where the big expense lies and those are mostly private hires. The SAR teams around me are first responders already on duty or volunteers. They still have expenses when launching a mission but driving a dozen people to a trailhead is cheaper than a chopper.