Implementing such a change has another problem: Who gets to have the time-zone that's noon at noon?
Are we going to let the British continue to get away with it? Even the excuse of "that's the way it has to be to keep things simple" would cause the French to revolt. Again. They still don't like to talk about the fact that it's Greenwich and not Paris that's the prime meridian.
Swatch's "Internet time" was a decimal system designed to mitigate the problem because no-one would have any idea what the old time was supposed to be, but people are used to the base-60 system. It didn't and won't catch on.
And it doesn't fix the "0 isn't my midnight" problem, which is pretty close to the original.
It also doesn't fix the "what time of day is it elsewhere in the world" problem, which still requires knowledge of time differences. You know. Time zones.