There's a whole lot of social conventions tied to local time, sunrise/sundown, and the circadian rythm in general.

Sure, it'd be possible but we'd have to concieve a lot of new cultural concepts to replace the ones invalidated by the shift to UTC, and find new ways to remind people that it's impolite to call people in the middle of the night.

In the long run, a list of time zones aren't that much more complicated to work with than a list of times when it's mid-day is in the major population centres on the planet.