I am amazed how many people on this thread are attacking me saying "Android Chrome supports push notification" when I said "Chrome doesn't support push on iOS". Are you even listening to what I say?
Every browser on iOS is just Safari with different UI (by order of Apple). No one else even could implement push notifications into their browser because only Apple has that control.
It's not that we don't hear you, it's that the reason you're in your position is because you're using a locked down platform that's trailing all other vendors in web technologies intentionally.