MobileFrontend allows us to queue notification messages to display after the page has reloaded. This is useful for displaying toasts after an edit has occurred. Under the hood it creates a localStorage entry that if present will be cleared and trigger a mw.notify message when that's done.
I think this is a useful feature. Having it in MobileFrontend means we can't use it in desktop.
The functionality in MobileFrontend's showOnPageReload.js should be in core. In particular I'm sure it is useful for editing and would DRY up some code.