I run strava, and rather than pay for the beacon feature, use Google’s location sharing. My battery easily lasts a day ride, and I usually carry a whistle too just in case.
I reckon if I’m capable of using the phone to get help and describing my location, I’m probably not in that much trouble. If I can’t use the phone hopefully my wife will remember I’m meant to be back, find an approximate location, and emergency services or passers by will hear the whistle (which I keep on the front of my camelbak so I can get to it with damaged arms) if I’m conscious.
I can’t understand why anyone would have to try to keep off the internet, and you can just put your phone on do not disturb to avoid incoming calls. That said, old phones are pretty durable and buttons make them easier to use, so a PAYG sim in one left switched off and charged in the camelbak could be a decent idea if you don’t want to take your smartphone out.