Pushing email and other notifications on a mobile device is viewed as the default position for most users these days. It used to be that we would collect our email when we wanted to, but for some reason that has changed to the point that we prefer to be continually interrupted by the beeps from our phones.
The reality is, however, that fetching email and other notifications is just as efficient as having them sent to us. Indeed, it is often more efficient because you get time to concentrate on what you are doing and only check your emails when you want to. It save battery life, time and enhances concentration.
Push is great for some things, such as important messages, but you can set up exceptions on modern smartphones to cope with these and still fetch the rest when you want to. Not every technological invention is as useful as the manufacturers would have you believe.