Most of the time the app is pushing them on you for engagement (youtube: LOOK NEW VIDEO!). But for important chats with important people, I sometimes want a notification when they send me a message.
I never treat text communications as real-time communications, and I'm not about to start now.
I'll never forget being awoken because someone felt the need to page the SysOp at 2 AM on the Compaq laptop running my BBS in my closet.