You're going to hate me then: I go a step farther than OP: Do Not Disturb mode 24 hours a day, 7 days a week. No notifications, no messages, no phone ring at all. I make sure my voicemail is never full. Leave a message and if it's important I will get back to you.
If I have a sick relative and explicitly expect an urgent call, I can easily and briefly turn off DND mode.
If the concept of a telephone never existed, and "Phone App" was invented today, it would be considered extremely intrusive and likely not (at least on iOS) pass App Store review. Think about it: Here's an app that allows any random person to cause your device to 1. interrupt whatever foreground app you have running with system-level UI (notification or full-screen takeover), and 2. ring and vibrate your device without your consent. If we weren't already familiar with telephones, we would never accept such an obnoxious app!