This would require unique time dilation regimes depending on your latitude - i.e. clocks on this regime would no longer track with an atomic clock

To make it simpler, we could make 12 PM solar noon year-round, use 24 fixed-size hours per day, and just vary our schedules throughout the year so that work and school times make sense.

In other words—leave the clocks alone! It's not the clock that's the issue here, but rather the learned inflexibility about arbitrary work and school hours.

Well, it's complicated in the sense that you couldn't work out the conversion without a computer, but on the other hand it's simple in the sense that the only parameters would be position on the Earth's surface and date/time.

Also, I've read that counting 12 hours from sunrise to sunset was in fact how several ancient peoples did it. They didn't even necessarily count hours at night, only watches.