For railroads, even at 40 kph, an east-west train would be subject to time shift (not in the Lorentz sense, it would just keep switching "timezones" too quickly). Given that the primary security element was "this train is supposed to pass this set of switches between this and that time and wait there, else it risks colliding with that other train running opposite," both accurate timekeeping and geographically wider timezones were needed (as in "the railroad will use its own time, Prague's lunchtimes notwithstanding").
Time zones were implemented in the United States in 1883. This was well after the use of telegraphs had become widespread, and after the invention of the telephone. While the telephone would not by able to make coast-to-coast calls for another few decades, the idea of communicating with people in other cities was already becoming commonplace.
My point was that the "messy" system the Times article describes would already have seemed reasonable to everyone, who already knew that people in other cities would have different working hours. What annoyed people was the "flattening" of the time zones, making it such that all the cities had to now synchronize their clocks to railway time, no matter what their local noon was. But this is the opposite of the point that the "one global time" advocate thinks he's making.
That is true, but it did not bother anyone, because fast long-distance communication either did not exist or was very limited (e.g. smoke signals) and syncing of clocks wasn't necessary in everyday activities; for a medieval person, the idea that clocks in Vienna and Prague MUST be synchronized would be as strange as for us the idea that everyone in the same city should have their breakfast at the same time. It just did not serve any obvious purpose.
There are only two exceptions I can think of.
a) people doing astrological horoscopes for someone who was born in a different place (a big thing among some nobility and royalty) would probably be bothered a bit by the time difference,
b) armies trying to converge on the same target at the same moment.