Your argument on this thread is incoherent. You begin by suggesting that GCM is problematic because it's a component of a larger platform library that gives Google control of Android phones. When it's pointed out that GCM push can be supported without that platform library, your argument shifts: it's the messages themselves that are dangerous. When it's pointed out to you that the messages are empty, you invent a scenario in which GCM push messages enable a kind of traffic analysis that on-the-wire traffic analysis can't already accomplish.

Were this my argument, rather than pointing me to a thread where my points were continually and reliably refuted, I'd take this opportunity to instead restate my argument clearly.