I woke up at 14:00 GMT. Did I wake up early, or sleep in?

A time without an associated time zone or location is always lacking sufficient information to convey the full context of what the time means.

Timezone issues arise when events cross timezone boundaries. If we use timezones, it can be tricky to know what specific points in time correspond to in other timezones without additional information. If we all use GMT, it's difficult to know what a time actually means without additional information.
Since we care about where the sun is in the sky, and also when events happen relative to one another, it's not an easy situation to just make work.

It's why a proper timestamp includes timezone offset information, since that's easier to work with that geospatial coordinate offset.