I am a runner and when I go for runs I don't take my phone with me. I have a Garmin watch that has music storage (which I also use for podcasts & audiobooks) and some basic navigation/mapping functionality (which I've never used). I run semi-long distances, up to and above a half marathon for training runs, and never really felt like I needed my phone. I guess it would be useful for emergencies, and when I ride my roadbike I do have it with me, but that's primarily because riding is more dangerous. The main thing I miss on my runs w/o a phone is snapping a pic every now and then. I would not use it for anything else as I don't make any stops (I run non-stop), and quite often I don't even wear headphones as I like to enjoy the sounds around me.

I suggest you guys try it. And yes, that includes if you don't run/jog, _try_ that as well, phone or not.