[badgers]

I believe there is a way to do this, if you use Do Not Disturb and make an exception for All Contacts.

[gergles]

Not really, because then you can't get any notifications you actually do want. (Turning on DND blocks every notification.)

Apple refuses to make it so you can actually manage how the "phone" can bother you, and I'm assuming they have some sort of deal with the carriers to be this way.

[yawz]

Interesting idea, but sometimes I do that when I sleep, so I would need that exception list to be small.