Let’s say people can’t agree on the time to go to bed, and each timezone declared war on every other timezone. Who would win in this conflict? What alliances would form, and will there be betrayal? What would the new world order look like with a standard time for everyone?
GMT+8 looks good with the entire population of China on its side. GMT+1 and +2 have large chunks of Europe and Africa and could be quite strong too. The timezones in the east and west coast of the U.S. might also stand a good chance.
Any war with this many aggressors who were all opposed to each other absolutely would just look like everyone killing each other at random. Even without nukes, it would be madness on a scale never before seen, resulting in a quieter, nay sleepier world.