As incredible as it sounds, there are benefits of switching off connectivity to your mobile phone. There are at least two instances of doing this in a typical working life. The first is to go completely switched off on weekends. This is ideally done with a couple of like-minded, and preferably sports-loving, people (to keep boredom at bay) and/ or with a good book. By Sunday, you feel refreshed. Of course, this works only if you have aligned in advance with your manager and other critical stakeholders.
The second is to pay complete attention during conversations and meetings. That means keeping your phone in silent (ideally with the vibrator off) while talking to anyone, and during any meeting that you care to attend. Nobody I know does that. Nobody except myself! I find it very distracting to glance fleetingly at my phone while someone is telling me something important, and I value the present. In meetings, this practice of keeping my phone in silent mode lets me listen clearly. In conversations, this lets me value the other party. And then I call back the interrupter.
It is not that I ignore what my phone says. I just like my time and attention as interruption-free as possible.