my parents never told us we couldn't use our phones at dinner, but they did explain that when we did it, we were signaling that what we were doing with the phone was more interesting/important than family dinner. I decided that wasn't the message I wanted to give my parents, so I would only pull out the phone for time-sensitive communications. a little bit of respect can go a long way.
I think it's okay to set reasonable limits on screentime. I don't think you should force your child to interact with you; that seems kind of unhealthy.