I had a mobile phone for a year and HATED it. Got rid of it about 7 years ago and have not, for a single second, missed it. As mentioned above, payphones are a disappearing option in emergencies, but I find offering someone else a buck or two to use theirs ('cause everyone else has one) has worked the three times I've needed it. Mind you, I'm old school, and still believe in the kindness of strangers.
I love the freedom that comes with not being at everyone's beck and call 24/7. I watch friends who join me in a walk constantly digging into their pockets to respond to inane texts. Often they respond with "Will get back to you later". Really? You couldn't have just, you know, gotten back to them later???
I'm not nearly important enough to feel that any calls coming in to me require an immediate response. The world just isn't gonna end if I don't take a call.
As far as the safety net aspect goes, I've managed to live, work, walk and drive myself around for an increasingly long amount of time, in cities, outside of cities, in the wilderness, in 3rd world countries, and have never considered myself unsafe because I don't have a mobile phone. I've never bought into the fear factor being marketed to us. And I truly believe that that is what's happening: people have become convinced that everything from not getting a flu shot to not owning a mobile phone to not micro-chipping their pets (or kids) is adding a huge risk factor to their lives. I call bullshit.