Chances of adopting a universal timezone are pretty much nonexistent for political reasons, and the switch itself would probably be a bit of a logistical nightmare. However, claiming universal timezone in itself would be any difficult to use does seem a bit disingenuous.
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.