Just take things to the logical conclusion - everyone should switch to UTC and quit all this screwing around with timezones and clock changes.
If you want to take things to their logical conclusion, we should be using a sort of UTC decimal time (10 hours in a day, 10 (was it 100? can't remember) minutes in an hour, 10 (same question as for minutes) seconds in a minute.
Switching to a single timezone would mean that days are upside down. Imagine some timezone where the sun rises at 23:00 and sets at 13:00. Let alone the fact that a decent chunk of the world doesn't even use 24 hour time (I'm looking especially at you, US!).
You just might convince me to adopt that kind of timekeeping, if "Monday" didn't suddenly become "Tuesday" while I was eating breakfast!
But seriously, every time someone floats the idea of worldwide UTC, I can't imagine they've thought through all the new problems that would arise.
We have different time zones, not because we're dumb. It's because the Earth is round. The time zones are an intrinsic property of {ball Earth} + {human biology}
If we lived in Flatland, it wouldn't be an issue. If we were robots with no circadian rhythm or desire, then it wouldn't be an issue. But we're humans on a globe. Different locations are going to be out-of-sync no matter what. Might as well reflect that in our timekeeping.
(EDIT: I'm agreeing with you, BTW. Just re-read this and it sounds kinda like I'm arguing with your comment. I'm not. I'm yelling at the strawman :)
Base 12 is better than decimal in every way. It divides cleanly by 1, 2, 3, 4, 6, and 12. Compare that to decimal, where you have 1, 2, 5, 10. It's much better for scheduling. With decimal you couldn't have a nice, clean schedule for a factory with 3 shifts per day for example. 60 minutes (which is a multiple of 12) gives you a lot of ways to break up an hour, vs 100 minutes.
I had a friend once rant about how we should switch everything to base 12. It's obviously crazy given the effort vs reward, but I think we would have been better off to have done so way back when.
Base 10 is so embedded in what we do, that a switch to base 12 is the kind of thing that would be done when we rebuild civilization after the first alien attack :-)