Jesus man, I'm in my early 20's and even I don't make sure to put my phone in my pocket just to go pick up the mail. What could possibly be so important that it couldn't wait a whole 120 seconds?
Nothing - but the same habit also compels me to carry my wallet & keys everywhere I go as well. It costs me nothing to carry it, and there are times where I've returned to my apartment after stepping out for a minute to find myself locked out.
My door locks automatically when its closed - so when if I were to forget my keys, I would get locked out (which has happened, which is why I always carry my keys).
I do that with my wallet and keys. I rarely take my phone out of the house though, and even leave it switched off for days or weeks at a time. I'm not sure what I'm missing out on by not having it available 24/7.
It's a very liberating feeling once you have 'trained' your friends and family that you are not dead nor hate them if a text goes unanswered for a few hours.
That is orthogonal to having a smart phone on you 24/7. I trained my friends and family not to expect instant replies (or me always picking up phone calls), but I use the phone also to read stuff, search for stuff, and note down stuff, so I do want it on me all the time.
I'm usually in the same place, and using my Linux desktop. I guess that's why I've always found it hard to get interested in phones: annoying devices with too-small screens, slow data entry and usually a locked-down OS with no updates.
Both myself and everyone I know have their phones on them 24/7, and next to their bed when they sleep.