> The only people who need it are Astronomers.
And anyone that cares about the relationship of the time of day and the position of the Sun.
Granted, it's not a lot, only a minute per century.
Yet high noon at my current location comes at 12:03 (1:03 with DST). It's three minutes off. If I lived further west in my timezone, noon would come much later.
How can people manage with noon off by minutes, yet want leap-second accuracy every 6 months?
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.