Computers don't really care about the current wall time. They just care about measuring time between events. If a piece of software about the current day of the week it's only because a person cares about it and wants to do something special on certain days of the week.
So, yes, time systems should be designed around the needs of people.
I believe time systems should be designed around the physics of the natural systems we inhabit. This may help us mere humans better harmonize with the rest of that which makes up our worlds.
This may sound a bit hippy dippy at first, but just consider how much light pollution effect other creatures, for a quick example.
Why not? Are you being considerate for alien life? As far as we know, humans are the only ones who are going to use it.