I think you hit on the right answer.
The justifications given above don't really make sense - "how would you know when to call Sydney" or "the sun being overhead at 10PM would feel strange". They are just rationalizations of a system that we're used to.
But everywhere around the world, people want the date to change at a time when most things are closed and most people are asleep - which coincides with night-time for obvious reasons. This is effectively more important than having the date change at the same time for all of us.