I have to say, if you are elderly what are you supposed to do if you don't have a mobile phone and the power goes out?
If I remember right on all my recent power outages I still had mobile service, and I do agree with Black Sheep here.
If anything mobile phones are safer, they more reliable (at least in my experience), batteries last longer so less likely to have a dead handset, and they have better water resistance to home phones so e.g. if dropped in bath for a moment it might still work.
I would say the one thing not really addressed is been able to fumble around the buttons in the dark or if blind due to lack of physical buttons, I am surprised there isnt an established emergency call system that bypasses unlocking etc. yet on mobile phones.