Classic counter example: storing business hours. If the store/exchange opens at 8:00AM every weekday in Somethingania/Foocity, you want to store 8:00 and the name/reference of the timezone. Because the store/exchange will still open at 8:00AM local time, even across DST, government-mandated timezone changes etc (largely, I'm sure there are exceptions but for stock exchanges there definitely aren't).

School times, times for religious services, lots of times are relative to local time, which itself is subject to change against UTC (sometimes predictable, sometimes not, the government gets to update the timezone and the DST scheme arbitrarily). So only ever storing UTC and using local time purely for display isn't a sustainable one-size-fits-all option.