This can matter when timezone definitions change, such as when a country decides to start/stop following daylight saving time.

If I schedule something for 1 pm 6 months from now, and a transition to/from DST is supposed to happen at some point during those 6 months, and then my country decides to not follow DST anymore or to follow DST year-round, once you update your timezone database and convert your UTC stored time to my timezone, it's going to either be 12 or 2 pm now. This is probably not what users want, unless they scheduled the event to happen a certain time interval after some other event that's not affected by timezones.

Data you store that you later want to analyse in a way that cares about the time of day.

E.g. when during the day is traffic at its worst, when is temperature highest, etc.