Give the way we structure our time zones, noon can only ever match the sun's zenith for some subset of people.
Your days will be longer than 24hrs from winter to summer solstice, and shorter from summer to winter.
You cannot have the same time system across an entire line if longitude.
Which sunrise do you pick? The equitorial one? 45 north? This may be more fraught than you were considering.
We could move from measuring time with a 24 hour clock to one based on solar angle.
We could also measure geographic distance in relative change of solar angle, combining our time and distance systems.
Some think it overly complex, but the increased geometry proficiency would save many lives.
I am far enough north that at some point as summer rolls around, I transition to sunset based structure, setting my morning alarm for 9 or 10 hours after sunset.
In practise, whether the sun is 15 degrees to the left or right at exactly noon doesn't have much practical effect on people in the way that it getting dark before they even can see the sky in the evenings does.
Anyway people should do this daylight saving forever experiment and contemplate these issues in the dead of winter. We can come back to this in a few decades.
All those standard start times are based on a world centered on solar noon. Maybe the semi ancients were onto something.
Eventually the noon reference became fixed upon, but it's only noon because it was easier to measure the shadow in that way. Other than a vague but unfounded sense of aesthetic need and the obsolete practically of synchronization with a sundial, solar noon isn't special.