Once exception: security related incidents. Critical software upgrades, fraud alerts, someone tried to access my account, credit card expired, severe weather warning, that sort of stuff.
In each of these cases (except software upgrades), you’ve set up such a notification (or did implicitly through a contractual agreement) yourself because you want to be notified in such an event. This isn’t so much technology reaching out to you, as a tool doing its job (which happens to involve notifications.)
Software updates, I don’t want notifications about either. At best give me a badge icon in the settings app or app store that I can check on my own. I’ll dig in and figure out what the badge means.