Open Source and centralized are orthogonal to each other. Signal is both, just to name an example.

An open push framework only makes sense (for battery optimization at least) if it's centralized, and all applications make use of it.

While Signal client app source is open, the server side isn't and the global system (and Moxie in particular) is notoriously hostile to federation or any sort of free interoperability. For a communication network, this reduces the benefits of openness to almost nothing, and, at least from my PoV, do not bring any kind of freedom or security to the users. While I can imagine a free ecosystem being somehow centralized, I firmly believe that Signal is on the contrary an illustration of centralization imposed against user freedom which suggest that these properties may not be so orthogonal.

>An open push framework only makes sense (for battery optimization at least) if it's centralized, and all applications make use of it.

Sure, from the perspective of a single device. But that doesn't mean all devices have to use the same push server.

No, you need to use a library that allows the user to configure the push server, which should be configured device-wide and communicated to the app server.

Exactly. I believe this is how Web Push works; the major browser vendors each run their own push servers, and the protocol is standardized.

That's a good point!