Like, what if you only need the date but not the time? You can use timestamp to store a birthday, but which in which timezone should you transform it back to date?

Or what if it is specifically about time in timezone independent way? You want to wake up ate 06:00 no matter in any timezone. Just something like alert.

You could use part of ISO8601 like 2020-02-02 or 06:00:00 to store exactly what you specify. But with timestamp, not so much.