That's potentially a good idea. It could even be hidden in the developer section, since those are the people most likely to notice.

Is there mention of this in any of the dialogs that one is asked to click "I have read and understand" that were not actually read? I remember Photos telling me that it was scanning the library to do their new layout after whatever update that was. That was to that specific app, and not a system wide notification, but it also said it would be paused until it was plugged in.

I could see a new something in the Settings that indicates post-OS upgrade showing migration status being useful.

Likely, yes. The thing is, the phone does not "heat up". Perhaps they throttle the whole phone down globally and let the background update processes run at a slow speed/low priority so they don't heat up the phone too much.