Once you accept that time and sunlight don't need to be linked - you can do away with timezones entirely. We only really need one time - UTC.
Actually, back in the day, there were no time zones. Only "Local" time mattered (12:00 Noon, being, well, 12:00 Noon when the Sun was highest in the sky and due south wherever you were)
I am not sure who first introduced the concept of a unified "Time Zone" but it might well have been Britain.
The issue was railway timetabling, though this had been a minor issue with stage coaches (mitigated by coach drivers carrying two watches one running slightly fast, the other slightly slow, timed to correlate with the speed of east/west travel and with different watches being used depending on whether one was traveling east or west.)
But trains traveled fast enough for this to be a real issue. so the railways adopted "Railway Time" IE everything was corrected for GMT. Station clocks would have two Minute hands. One corresponding to the local time, the other to GMT which was the time the trains ran oo. The further west one got from London, the greater the discrepancy between the two hands became.
Eventually "Railway Time" was adopted across the whole country, Probably when electrical communication (Essentially instantaneous) became commonplace and work place times had to be harmonized in a similar way to railway timetabling to prevent problems.