I think I know why. This is a battery savings thing for Apple. If you notice, the only account that gets the priority push now is, iCloud. By forcing you to a 3rd party application for instant emails, they dont have to support you, its not their fault or an issue with the battery.
Thats my thoughts, since all of this pretty much just started to happen on my wifes phone. I have a friend who bought 2 new eights when they came out, even returned one and never got all of this resolved. Just turned off his email alert because his alerts that there is a new mail, but nothing appears until several minutes after the alert.
My guess, this is yet another hidden fix like the battery slow down!