Notifications of new versions of LibreELEC are displayed. If you are using a stable build, a notification will follow when LibreELEC 8.x is available. Updates for alphas, betas and rc's are shown as well when using such builds.
Notifications of new versions of addons are displayed when addon updates are set to be done manually. Displaying version numbers as well is unnecessary for the majority of users. Version info can always be looked up if necessary.
Notifications of successful of addons updates are always displayed.
Info such as clock, weather can be enabled in certain skins. Is it useful to permanently see weather info during a video..? Personally, I doubt it. And, which statistics?
Enabling push messages is up to the addons IMO, not the core Kodi system.
Notifications for lack of storage and battery level are things to consider.