That's already false except along one line within every timezone (and that's assuming the timezone is properly set and not a convenient political or historical

That's already false except along one line within every timezone (and that's assuming the timezone is properly set and not a convenient political or historical fiction). Let's say your timezone is perfectly positioned, and "true" in the middle. Along its east and west boundaries, local noon is 30 minutes off. Near daylight savings transitions, it's off by about an hour everywhere. Local noon just doesn't matter that much. It especially doesn't matter to the second.