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Inagine going back hundreds of years to convince everybody in the world to use the same time. "No I know not everybody has a clock, but if you could consider sunrise midday that would make my job in the future much easier."
The reason we have timezones is because of the railroads. Before the railroads came in, every town would have its own time, typically set so noon is the time when the sun is highest in the sky. This really wasn't a problem, as back then it didn't really matter that the time was different in every little burg.
Then the railroads came in. They needed things running on a coordinated time table out of necessity, and having every town with its own time was unworkable. I'm sure the railroads would have loved running everything off of the same clock everywhere because that would be simple. But people were too used to noon being the middle of the day, so instead we got the compromise of having timezones so that the railroads can still run on a coordinated time table, but also so that noon is still approximately the middle of the day as people were used to.
So the solution is just go back to the 1800's and convince the railroads that timezones are actually silly and that they really should run everything based upon UTC. And if people want rail service to their town, they can just deal with not having 12PM being when the sun is highest in the sky.
Well, UTC didn't exist in 1800, it would have been GMT, and that might not have been too popular so soon after the war of independence. Even if you convinced all of the USA to use one time zone for the railways, it would be different elsewhere and you'd still get time zones.
Maybe you'd get further with the project with the airlines in the first half of the twentieth century, but I'm not sure that that level of internationalism would have gone down well in a rather war torn world.