I do tend to agree that this has a pretty good chance of creating more nuisance calls from people who are not in actual danger...I read the New York forest rangers reports now and then, and a big portion of the rescues involve clueless people who set off alone with no map, an hour before sunset in October wearing a tshirt and shorts.
Like, the moment you're sufficiently sure you might be lost or at risk/danger. Then at least they know you're out there and where to start looking from your last known location even if you don't need help yet. They might also be able to trivially guide you for self-rescue instead of the situation escalating into requiring rescue or becoming a much more complex rescue.
But if it's just a simply SOS device, then, well, yeah, it can become a nuisance because that can mean "I'm a bit lost" or "I'm quickly dying" and anything in-between and they have no way of knowing.
Someone with the knowledge and foresight to bring along a Garmin or PLB or something probably has a decent understanding of what it means to use it - waking people up and deploying expensive assets - and because of that I can see why they'd probably hesitate (it surely would trigger my "I don't want to be a bother" instinct).
I hope once every iPhone user has the same capability that it doesn't become an "eternal September"-like moment and flip too far the other way into overly casual use.
Regardless, you're much closer to the situation than I am so I'll defer to your expertise. Clearly, more communications in an emergency is always going to be better, so I look forward to seeing stories about how this new feature saves lives.
And thanks for your efforts in providing rescue services to the people who need them!