Why don't these search and rescue teams simply unblock their number so it identifies who they are?

I might actually answer my cellphone when out hiking if it showed an incoming call from, say, "Colorado Search and Rescue" rather than "unknown caller".

Cellphones don't work with standard landline caller id, but the providers (AT&T, Verizon, etc.) can send an ID if they want to. You think they'd be agreeable to do that for the limited number of rescue agencies, police agencies and other emergency responders who might care to ask. Businesses can pay to have their id sent out on cellular calls, so you know the providers have the capability.

Also, search and rescue teams could publish the phone numbers they might call from to local area residents (or post them at trailheads) so people could enter them as a contact in their cellphones so that the name would show up on incoming calls. Even a simple coutry-wide online database of search team names, phone number and area(s) covered would work. Get the word out and people could look up and enter ones relevant to them as phone contacts. What, we only have 50 states (plus a few territories) and how many rescue teams could a state have? A dozen per state would seem on the high end. That's a very small database. You could even do it with a flat text file sorted by area covered (state, then quadrant of the state).