IMO direct messages, using people's names in messages, or @them is a disruption and should be reserved for needing one. I hate being deep in work, and then being disrupted for something that could have easily been put in a channel that I could look at later.

Turning off notifications would mean muting people that are more respectful and might have a legitimate reason to disrupt you.

Sounds horrendous.

Seriously though thats a different type of communication though? Can you host slack on prem?