On iOS, apps needs to ask permission before they send notifications. If you missed that, there's also a single toggle in Settings -> Notifications for each app. There's no situation where you should have to "kill all the various types of notifications". While I agree a global "Disable Notifications" toggle would be nice, I don't think it's too much work to just tap "Don't Allow" when an app initially prompts you?

The iOS notification ecosystem is actually miles better than it was in the iOS 4-10 days, I think it's fairly user respectful now.