I tried looking at Universal or cosmic time by Sandford Fleming but it was not clear. I know there were competing proposals from the french etc. Did any country or group propose the rest of the world universally adopt their local timezone?
The Swatch clock company tried to implement the Swatch Internet Time about 18 years ago when the internet was just becoming common place. It was in a decimal system and didn't have time zones. They even had watches made that displayed the time in ".beats", the name of the daily division, but they never caught on.
The closest that I know of is that Hitler imposed one time zone across the Reich. This led to early morning attacks on the Russian front starting at, say, midnight which soldiers found odd (see Guy Sajer, The Forgotten Soldier) although probably made a lot of military sense.
Hitler persuaded Franco to set Spain on to Berlin time, which it still is today (and a subject of debate in Spain).
Thus one can argue that Hitler was likely a proponent of a single time zone and had Germany won the war might have been implemented across a significant part of the world.
This might be slightly off topic but the US Military uses Zulu time in conjunction with regular time zones. Zulu time is just a common time used by members of the military located across the globe to make coordination and planning a lot easier.