Consider: in a world with timezones, all you need to know is what time’s in Melbourne right now, and what time Steve’s typically awake these days. In a world without timezones, all you need to know is what time Steve’s typically awake these days.
What about 0000 hitting in the middle of the day? Well, a bar I recently went to is open “Thu–Sat 8pm to 4am, Sun 8pm to 2am, Mon–Wed off”. In a world without timezones I don’t think anyone would be confused by a sign like “Sun–Fri 2300 to 0500” at a post office or barber shop.
We have tools to deal with timezones, so that complexity is pretty much hidden these days. That said, I can’t help but notice every now and then how leaky the abstraction is. Humans are not machines—more and more people work independently or on flexible office hours, many businesses are routinely open different times depending on the season even if the country uses DST, and so on.
-I was once told (and found it too amusing to verify the truth of it!) that as GMT took hold as the go-to global time reference, the French grudgingly complied, but referred to it as 'Paris time minus seven minutes and twenty-six seconds' or something to that effect.
Perhaps the writing is silly, but there's nothing silly about the point the point that of course people will maintain the solar day for daily life, and abolishing timezones will basically break time for most people (especially those whose "midnight" (and so the changing of the date and name of day) will land during the solar day).