This is just how push notifications work on iOS and Android. The app requests a push token from the operating system, sends that to its backend and stores it against the user's identity. To send a push a message is sent from the backend to a push service maintained by Apple or Google, who then deliver the push to the phone in question. In the case of Signal, their backend cannot access the message content, so the notification does not contain this, i.e. it's not MITM.

On iOS in particular background modes are finicky and you cannot generally have an continuously poll notifications in the background. Further, if every app did this battery drain would be significant.