Earlier quoted context omitted.
Push messaging is a service, just like anonymous proxies are a service. It doesn't make sense to put them into a platform if they can be built on top of the platform. It would make sense to put something like this into iOS because it can't be built on iOS. It doesn't make sense to put it into AOSP.
Earlier you said AOSP had a framework for push notifications, a statement found to be false when checking the links you provided. Now you say it doesn’t make even sense to put this feature in the platform, confirming that you were lying when you said it already was part of the platform. Why are you talking about iOS?
> Now you say it doesn’t make even sense to put this feature in the platform
Of course it doesn't make sense to build that library into the platform.
> Why are you talking about iOS?
iOS doesn't provide the ability to make this possible, which is probably why you are so confused.