@uber - The biggest problem with that plan is that it would weird people out too much. For half the world, the day would switch (say from Tuesday to Wednesday) sometime during the night, and they would be able to adjust to it. But for the other half of the planet, the day of the week would switch sometime during the daytime, and that would be much harder to adjust to. What would your weekend be, (1) part of Friday, all of Saturday, and part of Sunday, or (2) part of Saturday, all of Sunday, and part of Monday? And there would be a lot of objection from religious groups. If you want to strictly observe a particular day of the week as holy, it wouldn't work well at all if it included the end of one period of daytime plus the beginning of the next period of daytime.
I recall reading some sf story in which the world had switched to just having 4 time zones instead of 24. That would still call for some adjustments and weirdness, but it wouldn't be as extreme as just having one time zone. That idea *might* work, but it's always hard to make a huge change like that. Especially since every country in the world would have to buy into it.