Earlier quoted context omitted.
That would require keeping a connection open to the mail server 24/7 which is a bad idea.
Why a constant one? Why not on WiFi only? Push notifications also require a constant connection as well, I think?
https://news.ycombinator.com/item?id=9901686 (HN thread where Rob @ FastMail dives in depth why push notifications are superior to IMAP IDLE)
https://stackoverflow.com/questions/17262511/how-do-ios-push... (How do iOS Push Notifications work?)