Obviously there are two aspects to this that are getting confused here: time versus "at what point you are during the daily rotation of the earth". We use those two things interchangeably, but obviously they are not really the same.
Every longitude on earth is at a slightly different point in the earth's rotation (relative to sun position) at a given timepoint. So as someone pointed out, "sun noon" in Pittsburgh and Philly occurs at different times even though they are in the same time zone. So you need to adjust our time reference because otherwise it would be chaos (as other have pointed out).
But I think what you are proposing is to adjust everyone to the same reference time which would be independent of the "sun time." So it would be pitch black at "noon". The problems with this would be related primarily to biology. Our bodies like sunlight and you would find a higher instance of health issues (including depression) if you forced people to become nocturnal.
So can also probably appreciate the political issues this would present (i.e. who gets to live in the daylight); a microcosm of this can be seen in China:
https://www.theatlantic.com/china/a...has-one-time-zone-and-thats-a-problem/281136/
So, yes, sorry this is a dumb idea.