Conversation - the high-bandwidth, real time communication between individuals is supposedly the source of human empathy, the learned component, the training ground, with a few studies mentioned. Conversation is what we crave. What we really need.
Connection, is a poke, nudge, wink, smile, heart, like, follow, mass email, one to many posting, a tweet, whatever.
The offline aspect matters, since there is body language involved and hopefully attention.
Interesting perspective here: by sing phone messages less, you might strenthen your relationships. You will focus on the ones that matter (the ones that persist even after not using messages) and you would seek more high-quality ways to engage with them.
You cannot replace conversation with connection.