why not start work an hour later? Are these "special" (00:00, 6:00, 12:00: 18:00) moments of time of such psychological importance?
It is convenient in some regards to have fixed time points around common human activities.
For example, if you book an airline ticket with an arrival time of 13:40, you know with a reasonable degree of certainty that this is in the day, that businesses will probably be operating, that you might have time to do some shopping etc, because 13:40 is "early in the afternoon" and you know what "early in the afternoon" is like. When you are at this place, it is also easy for you to schedule your day, because you don't have to do any mental gymnastics such as "what time is midday here?"
If we all just observed UTC (which in a multiplanetary situation really would be "UNIVERSE"al even if it was adjusted for Earth days) your arrival time of 13:40 could have you arriving in the middle of the night which would be a bit inconvenient.
So, as annoying as it is to have timezones (and it's very annoying for a programmer!), it does make life easier for people to be able to specify time-of-day around the world (as opposed to moment-in-time which is why we have UTC).