I have a mobile, and it is a very useful tool. When I am out and about, I am able to recieve calls from doctors etc, which can lead to me getting cancellation appointments rather than waiting months to see a specialist. A mobile phone also means that in an emergency, I can be reached - so if I was out, and (god forbid) something happened to my DS, my DP could call me and I could get to him straight away.
It is also useful for trips out - rather than risk missing someone by arranging a meeting point, I can simply call them and ask where they are now so to meet them there.
I don't think it's possible to be unreasonable to choose not to have a particular item as long as you don't insist others follow your lead, but I do think that some of your reasons are a little misplaced. Having a mobile phone does not mean you have to be its slave. My nan has a mobile which is always turned off, unless she is out and about and needs to call someone (and there isn't a payphone). You can't get through to her, but if her car broke down in the middle of nowhere, she wouldn't be stranded. My other nan was in a car accident last year in the welsh countryside, and broke her wrist. My cousin was in the car with her, and was not only able to ring for help, but could take photographs of the damage on the phone to be used as evidence in the insurance claim. His mobile phone was a valuable asset, which he controlled, and usedto prevent them being stuck in the cold.
I would never presume to foist a mobile phone on someone whi didn't want one, however, so I can honestly say that I think the people who try to get you to use one are being unreasonable if they do anything other than make an offer before knowing you don't want one.