Use UTC + convert to local time for display if the time is a global event, i.e. something that happens at the same time everywhere. E.g. an online meeting, conference start time, missile launch schedule, etc.

Use time + timezone if the time is always local to a particular user and should follow their time zone. E.g. wake up alarm, eat breakfast schedule,

The problem is these definitions are already a bit fuzzy and it's not always clear which type it is even to the person creating it.