I think push will end up just being a failure for a few reasons:
I don't think it will end up a failure, but I could see it not satisfying every developer's needs. Also, I agree that notifications need to be less intrusive and they do indeed appear stone-aged.
First, I'm sure Apple has thought of most of the possible scenarios that push notifications don't cover. For those they hadn't, I'm sure some developer like the Pandora or ToDo app developers have let Apple know that push notifications don't fill their needs.
Second, I think the next logical step is for Apple to allow developers to add to the internal system notification daemon. This would cover all ToDo apps, timer apps, etc. by allowing them to set internal timed notifications through iPhone's current scheduling process without adding any additional overhead. All the push notification methods would be allowed: sounds, badges and pop-ups. Allowing a ToDo app and a timer app to actually run in the background would create three processes where the current active one (for internal calendar, timers and alarms) would suffice and reduce battery use and system resources.
A potential problem is that background apps can be closed - even accidentally. While this is technically on the user, you can never accidentally close an important notification with Apple's implementation. Say a stock trader is waiting for a limit alert on AAPL but accidentally closed their stock application last night. On the iPhone you still get your push notification limit alert - on the Pre, you don't.
Now we are left with the non-notification style applications, like Pandora. I'm guessing since Apple created the iPod, they're not too concerned about Pandora while clearly Palm would be. There's also the potential that Apple has their own streaming music solution waiting in the wings. But there are many other non-notification applications like a turn-by-turn GPS or fitness/run-tracking applications which would be pointless if you received a phone call in the middle. However, I'm sure that Apple will implement true background/multi-tasking soon. They already do with many of their applications, like the iPod app. But I think by urging developers to use the more system friendly push notification server when applicable, Apple is creating a better experience for when they do finally allow other applications to run in the background.
Finally, Apple improved many situations and ignored some. But I don't think push notification's going to fail for what it was intended to solve. The real advantage of background applications would be reducing the time to close and load and close and reload applications. In the mean time, I don't see a it killing the iPhone's market compared to Pre.