There is a massive technical benefit for all apps to use the same push server.
If many different apps use their own push server, a connection has to be kept open to each and every server, and each open TCP connection costs quite a lot of battery (since the system has to wake up to receive keep alives)
If many different apps use their own push server, a connection has to be kept open to each and every server, and each open TCP connection costs quite a lot of battery (since the system has to wake up to receive keep alives)