The line between "user initiated" and "app initiated" is not always that clear, but I agree with your general sentiment.
As some examples to consider: explicit one-to-many communications, actions that might warrant a notification where users explicitly dispatching communication would be cumbersome or undesirable (think mobile games).
One-to-many communications should generally fall in the category of “person communicating with me through technology”, which is ok by my standard. Then my anger turns to the person who may be doing the one-to-many communications inappropriately (analogous to shouting in the library or sending junk mail) and not the software.
> actions that might warrant a notification where users explicitly dispatching communication would be cumbersome or undesirable (think mobile games).
huh? Why is my mobile game sending me notifications? No thanks. (Sounds like a perfect example of something I’d hate TBH.) Mario RUN did this once. Sent me a push notification to… play more Mario RUN. I uninstalled it.
If you're playing a mobile game with friends, presumably you care when it's your turn. I certainly do. I wasn't thinking of single-player games, I agree there's basically no reason those should be sending push notifications.
As some examples to consider: explicit one-to-many communications, actions that might warrant a notification where users explicitly dispatching communication would be cumbersome or undesirable (think mobile games).