I really don't understand why anyone wouldn't use push when available.
I wonder the opposite. Why would I want to let emails dictate my behavior? I am an avid email user but honestly, I control when I get my emails and read them and reply. I have zero interest in having my phone ping me anytime an email is sent to me.
I have my settings to manual and check emails in the early morning, just before lunch, sometimes mid afternoon and then again late in the day. Each time I selectively reply at that same time. Otherwise, I tend to reserve the majority of my replies for either late morning or late afternoon.
If it's urgent, call me; but understand that my day has an agenda and email isn't going to drive my behavior.