Local noon is measured by meridian passage (a line) and not just the zenith (a point, directly overhead). I assume that is what OP meant...have clock noon be close to local noon. It’s a complicated issue, particularly long term, for example, where it then bumps into the move to get rid of leap seconds.

Exactly. The usual timezones are set up with the general intent that 12:00 is close to the time when sun is at its highest point in the sky. That is how our time historically was calibrated and I don't see why that needs to change if daylight time is abolished. It is a good reference. What else would be a better reference?