Not as simple as that because first: Timezones make it pretty obvious that you have to think or even calculate if it’s currently the day or middle of the night. If you want to call someone in another country it’s obvious that you’d first have to figure out their local time. If everyone used the same time than this would be easy, but you would’ve still have to figure out which time range is day time and night time so no benefit there.

For a lot of countries that would also mean that every “solar day” will be two calender days. You wake up at 19:00 March 1st. and just before lunch the date switches to March 2nd. It would be a mess.

That’s not the same thing and would lead to calendar drift pretty quickly.

You are wrong ;-) The push stuff is just used to signal the receiver that there is a new message. No meaningful data is sent that way. Not even an encrypted message.