The problem with only having one central clock is that you no longer have relative time. Right now, I can say something like "I woke up at 11am", and you understand what that means, regardless of which timezone I'm in or you're in. It means I woke up late.
But now imagine I said "I woke up at 16:00 Z." That's meaningless without the context of what timezone I'm in. That could be early, it could be late, it could be waking up from a nap in the late afternoon.
If you force people onto centralized time, then they'll still start using arbitrary (and worse) measures of relative time, like they'll say stuff like "I woke up two hours after sunrise".