I went about six months without cell service a few years ago. The only deal breaker is this one - that lots of services require SMS authentication and won't accept Google Voice/similar. GPS navigation is a bit worse, because you have to pre-download the maps and don't get realtime traffic. You also can't be contacted when you're away from wifi; this wasn't a problem for me but I can imagine if you had kids or something it would probably be another deal breaker.
Never been happier, and does not get in my way of doing anything as an owner of two tech companies that frequently travels. Phones are still optional for virtually everything in the US, though it sometimes requires talking to a manager.
That's a good reason for not carrying a phone, but getting a cheap SIM-connected device and leaving it at home next to their computer shouldn't reveal any more information than they already are by using their home internet and VOIP.
