I don't like to be without a watch. We have large clocks in most rooms here at home. Time matters to me and I stay conscious of the time. Most of my work has been scheduled by minutes and I had to pay attention to the continual passage of time to fit in with other teachers and their lessons.
I have read that the railroad and planning the departure and arrival of trains was virtually impossible when each town set its own time based on the sun. All my life the US has had four large time zones that cover the country: Eastern, Central, Mountain and Pacific. They went into action on November 18, 1883. But don't forget the scattered time zones of the US territories. You can see them and the times there at time.gov.
When I studied the history of psychology, I learned about the history and science of human perception senses. It turns out that scientific astronomers needed precise time measurements in order to study heavenly events.
We visited Big Ben in London, a very famous clock. It is an "hour" clock, striking on the hour. I think it did so before clock "hands" and the round clock face that we are familiar with were developed. I wondered at the idea of having only signals on the hour, without minutes or seconds. I imagine radio "broadcasts" had influence on the need for finer measurements of time.
Our computer project in grad school was to develop a Fortran program that gave the difference in days between any two dates. Our professor was known to be a weird, unpredictable thinker and we started guessing what he might call upon our program to do. The Pope's advisors informed him of the strong need to fix the calendar which had gotten out of whack rather badly. Eventually, he announced that Catholics needed to erase 10 days from the calendar so that tomorrow was not "the next day" but a day 10 days into the future. There were riots! How dare he "steal" 10 days ("TEN!") from our lives!