We do have a more-or-less universally accepted “world time”: Greenwich Mean Time (GMT), or Coordinated Universal Time (UTC), as it seems to be in vogue to call it now. (OK, I admit I don’t know the story behind the differing names. I’m open to enlightenment.)
I’m not reading the OP in the same manner as some of the posters who have responded. I don’t think it’s being suggested that the whole world adjust its living schedule so that we’re all working or sleeping simultaneously, regardless of the presence or absence of the sun in our local sky.
I think he’s (I’m guessing your gender, horhay_achoa - please forgive me if I’m wrong.) asking why we don’t all set our clocks to UTC, while still scheduling our lives more or less in accord with the sun.
Under this proposed system, the west coast of the US would still go to work, go to bed, etc. some eight hours later than folks in England. We’d just have our clocks set to the same time as Londoners. The “8-5” business day would start at 4:00 p.m. and end at 1:00 a.m., according to our clocks. The sun would be highest in the sky at about 8:00 p.m. - roughly the middle of the business day, and about when we’d be eating lunch. If you didn’t look at a clock, you would never know there had been a change.
The upside to this? As pointed out in the OP, “I’ll call you at 2:30 p.m.” would be completely unambiguous to anyone in the world - all clocks in the entire world would read “2:30 p.m.” at the same time. Since I’m assuming UTC, at this time it would be mid-afternoon in London, and about dawn in Los Angeles.
The downside to this? Pretty much what friedo pointed out. As things currently stand, if I’m told that if it’s 1:30 p.m. in Tokyo, or Kabul, or New York, then I can pretty reasonably deduce that it’s in the middle of the day, businesses are likely to be open, and I’m not likely to be waking my friend up if I call him. IOW, I can do a quick calculation and know pretty much where in the “daily cycle” a given city in the world is.
The proposed system would lose this. The calculation would not be necessary to obtain the “local time” (what clocks say) in Sydney, but since that “local time” (which is simply UTC) has no simple connection to daylight or daily schedules anymore, it’s pretty much useless knowledge.
Neither way is necessarily invalid. But there are tradeoffs involved with both, and for daily living I think the existing system is clearly superior. Like kunilou pointed out, organizations that find the “one-time” method suits their purposes better can and do use it.