What if the story is from a week ago? Yes, your 3am happens at the same time as their 3am, but your 'night' is still their 'day'.

You'd have to intuitively know every time zone and their offset in order to have an immediate understanding the way you do now that 3AM is the middle of the night. It requires an additional question or lookup table, which makes it objectively worse of a system for humans to use and remember.