Call me crazy but won't we need multiple moon time zones to differentiate day and night?
Discussion
Only if you want to keep this tradition of fixing midday to when the sun is at its highest position. Which doesn't really work out on earth anyway, if you want to be more precise than to the hour. So why not just keep one timezone and have night and day at different times?
Because then you would need to cross reference your location and global time (the only kind of time, since there is one timezone) in order to know whether it is light or dark outside. This just doesn't work in practice.
If you can actually solve this problem ( which I don't think you can do in a general way) you'd be better off getting rid of time zones entirely and operating on unix time.