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Why not have 2 time systems. One Earth Standard Time system for scheduling with different parts of the world and one system that is centered on solar noon at one's longitude and is updated daily at solar midnight, for daily awareness and routine activities. This system would count up from -12:00 at solar midnight, reach 0 time at solar noon and proceed to count up from there towards the reset time around 12:00.

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> One Earth Standard Time system for scheduling with different parts of the world

That's pretty much what UTC does. The aviation industry does everything in UTC for example, and you convert to local time as required.

> one system that is centered on solar noon at one's longitude and is updated daily at solar midnight

We have that already, it's called (local) Mean Solar Time.

How would that work north of the arctic circle? Would it be 300 a week after the sun came up?

There would still be a solar noon (sun at zenith) unless one was directly at the pole. Admitted, it would be more difficult to visually tell, the closer one got to the pole.

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