Even now, obtaining solar noon is comparatively easy. Then add half of an earth's rotation* (slightly affected by the earth's orbital period too), and that's midnight.
In the days of candle light, midnight wasn't a crazy time to draw that diving line. However these days even people with crazy early AM weekdays to avoid commutes sometimes cross over midnights on the weekend.
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You are correct that the modern world really should just start counting the day at like 3 or 4 am, and continue counting past 2359 to almost 2700 or 2800.
I guess I am arguing that "morning" "midday" "evening" and "night" should hold no official definition, since they are much more about the vibe rather than an absolute position on the clock. However, if they do remain as official definitions, they should be heavily revised.
"I woke up very early in the morning at 4am to start work at 5."
This is what really grinds my gears with the official definition of "night" and "morning".
Tuesday 21:00-23:59 is considered "night", and then Wednesday 00:00 is considered "morning", which is highway insanity to me. No one would say they were going out 'till "Wednesday morning" if they went to the pub until 02:30 Wednesday.
IMO it only starts being "morning" around 05:00, maybe even 06:00.