Without a cell phone you are still unreachable, so how exactly is this solving that issue?
The real problem here is that the people contacting you do not respect your desire to not be on-call 24/7. In my opinion, this lack of respect is good enough reason to not feel bad about ignoring them. Put your phone on mute and stop letting inconsiderate people push you around. Or just continue not having a phone because that works too.
I can't upvote this hard enough. If someone is calling me, their name pops up on the screen. What if I don't want to talk to them? I don't answer! If they leave a voicemail? I'll check it when I feel like it, and if it's not important, I won't bother with it. This article does hit one nail right on the head though, and it's the real source of the problems - when did people forget that cellphones serve them, and not the other way around?
The real problem here is that the people contacting you do not respect your desire to not be on-call 24/7. In my opinion, this lack of respect is good enough reason to not feel bad about ignoring them. Put your phone on mute and stop letting inconsiderate people push you around. Or just continue not having a phone because that works too.