I didn’t find it when I looked for it just now, but I recall reading how clock synchronization was a major improvement for rail transportation.
Of course the impact would depend on how much drift there was and how long it went uncorrected. What might be only a relatively minor annoyance for a passenger train not being on schedule, might be a financial hit for a freight train.
For a retired person losing a second a day probably not much of a problem. For a factory losing an accumulated few minutes of productivity a year, more so. If the stock market works like I think it does, not knowing the exact moment the closing bell rings could mean a difference of millions of dollars.
I think where synchronization would be crucial is coordination of military events. Clocks not being synchronized to the split second could result in a National Security risk.