I live without 3G on my phone, though I still have a SIM card for receiving "emergency" calls. I haven't topped it up though, so I can't call out.
It's been wonderful to make me focus on face to face conversations with people, rather than checking notifications all the time. I ask them to add me on Facebook, or make a note of their email address. If I can get online, I use mbasic.facebook.com with no ads, which loads quickly on an old phone.
My phone wakes me up with an alarm, but I'm not flooded with depressing Apple News first thing in the morning.
On the bus, I read books (the Bible and others, Edward Snowden's autobiography last year, currently The Shockwave Rider). I also browse offline Wikipedia (personally Wiki2Touch, but I've heard good things about Kiwix). I use Galileo Offline Maps with MOBAC-scraped tiles, without turn by turn directions.
Battery life is significantly better without 3G, and makes the old iPhone 4S quite usable.
Google Voice is often allowed for 2FA, and I use that when I need to receive SMS (e.g. TransferWise).
I could go without a SIM card entirely, but for the rare occasions when I do need to receive a call (e.g. I agree a place and time to meet someone, and they're late), then I still keep it in my phone.
It worries me to read that the US immigration department are using anonymised cell tower histories to trace people, but I don't know if removing the SIM card would solve that.