Excellent question. I have thought about this a lot. I love sundials.

Timekeeping is really three problems in one: scheduling, tracking elapsed time, and chronology. Over time an approximate solution for all three problems has emerged, UTC. Yet, if we address the problems individually, it really hasn't been a good solution for any of them.

The human schedule is innately tied to the day/night cycle, so it seems only natural that we should schedule events around the sun. Solar noon doesn't happen at regular intervals due to day length oscillating, so our ideal scheduling solution must treat days as having varying numbers of seconds. I like the idea of scheduling events hours and minutes before or after local solar noon. With modern communications technology, we know the local solar time at every location and can adequately predict travel time to the scheduled location. So for example, you would input "meeting in Chicago, -2:00" on your calendar to represent 10:00 am local solar time in Chicago, and your calendar app could output your scheduled departure in your local time wherever you happen to be.

When it comes to tracking elapsed time, it's really just a problem of having a standardized unit and a device that accurately tracks those units. So, we basically have the solution for elapsed time, but when we track it with UTC, we're unnecessarily dealing with leap years and such since we also want to use it as the calendar... annoying!

Chronology is where things really get interesting. With special relativity, we now know that time between events is subjective. If a civilization is sufficiently spacious or if people travel sufficiently quickly, there is disagreement regarding when things happen. The only robust solutions to chronology would involve a consensus mechanism. Time chain? Maybe...

Anyways, we need three separate timekeeping systems. It's the only way.