First, your app will now require servers somewhere that will send the desired app notifications to Apple’s server. Few developers will pay for that upkeep.

Second, if you’re out of data range, say on an airplane or ship, then any app that needs notifications won’t work. So much for reminder timers and such as that. Oh gosh, forgot your wife’s birthday on the cruise because no comms available?

Finally, people have been turning off push email because it chews up battery in their situation. Who’s going to turn on push notifications that might do the same?