I realize that changing everything to a different time zone would cause the zenith to be at different times, as opposed to 12 noon. I do, however, believe that the benefits would outweigh the drawbacks.
Benefits would be less confusion among time zones, changing times and the like, as well as easier synchronization of computers. Drawbacks would be not having it be the zenith at 12 noon, which isn't true half the year anyway due to daylight savings.
By this method, if the general area would normally be 7am for the zenith, the listed time would be 4am to 12pm for the working schedule, even if the time relative to the sun would be the same. People would get up at what's listed at 3am, just as the sun is starting to rise. This might be confusing since I'm not really sure how else to explain.