It's astounding to me that the default behavior on the gmail app is to actually push notify on every email, and that millions and millions of people leave this on.
It's not every email, it's just the ones in the main inbox (as opposed to notifications, promotions, social, etc). At least for me, it usually maps almost perfectly with human-sent emails, so it's a good feature because I very rarely check my email manually.
It's pretty rare for me to receive more than a couple notifications a week at most.
At least with iOS you get asked the first time you install an app whether you want notifications or not. Android allows them by default, and apps are not shy to spam you to get to open them.
Phones must be insufferable for most people.