Spotify in my car, gps/maps when I'm out of town, google results, HN, etc...I'd miss it sorely if I ditched it.
I could spent a lot of time and/or money setting all of that up in "offline mode," essentially. Mp3s, some map software, wikipedia offline...but in the end, we really can't trust pretty much any of the hardware available, so it might check in on every open network or something.
I'd totally splurge for an anonymous plan, with a trusted data provider, and open hardware platform.
Note: I did go 3 months with no phone a couple of years ago while I lived in Costa Rica--but I was either on my PC or at the beach. Never wanted a phone.