Lots of phone carriers whitelist that server of theirs to allow it to wake up phone unprompted from idle while typically only allowing phone-initiated connection to stay active, and they also tend to block most incoming connections once the phone has been inactive for a while.

While it isn't technically hard to make something distributed, to also make it work well can be troublesome...

Yet another reason I want home servers to become common, as your phone could automatically request that your carrier whitelist your chosen trusted nodes such as your home server.