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.
I understand having a separate time for Mars or other planets as they have their own cycles.
- It's also weird the time on the moon would have to account for variations in earth rotatoin speed (as UTC does) - Time on the moon actually goes slower due to relativistic effect - the effect is small (in tens of microseconds per day) but measurable.
We can surely skip one second every 27 years on the moon if we are able to add 1 day every 4 years on earth.