If the ps3 is constantly connecting to servers even when we're not logged into PSN, then why do we still have to sync our trophies. -_-
It's because of the way they set up the trophy system; there's actually a fair amount of data being transmitted depending on the number of trophies (amount of trophy data) being uploaded to servers and then downloaded back to the console.
You'll notice this if you ever download all trophy data from a user account with any decent number of trophies onto an unsynched console.
Automatic syncs would cause extra network traffic during play although there's no reason why they couldn't have the data sync immediately after exiting a game. Or why they can't have all downloads automatically install for that matter. I won't venture to guess why these quirks exist.
You can tell you're always connected to PSN servers even if you are not logged into PSN because the updates remain active unless you disable your network connection altogether.