See discussion elsewhere on this thread. Basically, most people care far about understanding roughly the "time of day" with respect to sleep/business/etc. than coordinating complicated international schedules. (For which UTC is sometimes convenient but even for frequent travelers is a small part of our typical year.)
Obviously, things would confusing to the point where it might not make sense to make the switch. However, after all the chaos, everyone's intuition would adjust to match their local longitude.
It would be a little awkward to decide what "time" to start the day though, but it's not like midnight is the greatest time to start a day either.
