Which means that time changes slowly enough that we don't notice. At some point everybody goes work half an hour earlier because it makes sense. Schools start earlier, shops open earlier. It doesn't have to be coordinated worldwide. Every region or even town can have its own customs. Then people notice they are in the wrong time zone and a country moves to a different time zone.

Statistically, nobody on Earth knows what UTC is. People know about their local time zone and how it related to time zones in other countries. Where the position of the sun is relative to UTC, almost nobody knows.