I worked with a guy who was in his 30s and never had a mobile, he just didn't see the need for it. Fair play to the guy, he felt the same way as you about it in terms of people assuming you can be contacted at all hours. People would always have his home number or his work number, and chances are if he wasn't at either place then he was doing something that he didn't want to be interrupted at.
I could probably do without if I had to, not tried though.