The birds aren't cheap, the rescue coordination centers (they know who to talk to, they have no ability to actually go into the field--although that's not always needed. Garmin recently mentioned one--SOS comes in "found lost child". 25 minutes later, SOS comes in "lost child"; all they had to do is direct them to where the other was) have to be staffed--and both are private.

If the government was running it, maybe.

Even government-run services cost money (usually much more than private ones). And the government gets its money from us, not from the sky.

Yeah, but the government can collect money via taxes, which allows it to solve coordination problems that would be more difficult for private companies to solve.