If you asked me, Safari is the centerpiece of the iPhone and always has been. It's even more important than the ability to run third party apps.
It was the first phone browser done right, and is still arguably the best. Outside of the phone operations, I would trade away every possible feature of iOS for Safari.
Notifications is an annoying piece of crap for a lot of people including me. That isn't to say the previous generation of alerts were not worse, they were.
But I highly doubt that many people think it is THE cornerstone feature. For some, like me, it's Safari. For others, it's FaceTime, others the camera, etc.