There is no significance to the number 12 on the analog clock outside it being painted on top of the clock face. And even that is completely absent in the digital clock, where hour 11:00 is the same as 12:00 or 13:00 in significance.

So there is zero astronomic reason to fixate noon to a particular number if doesn't suit us, humans.

I'm just saying that astronomic argument is kinda meaningless for the DST discussion, the only thing that matters is manual allocation of light time for the most people as possible, so that a majority of population would receive highly beneficial natural light as much as possible. When the solar high point would happen in that scheme should be entirely irrelevant.