Things would be worse without timezones since it's not like everyone will go to have a 09:00UTC - 17:00UTC workday, they'll work based on the local solar time (which is why timezones were invented in the first place). So without timezones you'd have to remember "Let's see... it's 14:00 UTC here now and I just got to work, so is my west coast colleague awake yet? Hmm.. let me look up the sunrise. Oh yes, here it is, his local sunrise is at 14:30UTC so he's probably still in bed, I guess I better call him later. I wonder when he'll get off work...hmm...if sunrise is at 14:30, he probably starts work around 16:30, so maybe he'll be home around 01:30UTC.
Fixing the calendar is hard since (like timezones), years are tied to natural phenomena and 365 is only evenly divisible by 5 and 73. So you could have five 73 day months (plus a leapday), or maybe could go with 13 months of 28 days to give 364 days. Just make the extra 1.25 days a holiday.
But with timezones you still need to work out when your west coast colleague is awake. And the calculation, when you think about it, is much more confusing with timezones.
Also, a lot of people don't work with the sun, particularily since the time of sunrise changes with distance to the equator and time of year, so sunrise and the start of work have very little to do with each other in most parts of the world.
Think of a colleague who might be stuck working in Regina, Saskatchewan, Canada, time zone is CST (UTC-6h) and they don't use daylight savings. In the middle of the summer there, the sun gets up at about 5AM, in winter not until almost 9AM (the further north you go, the more this effect gets exagerated). If you want to know his office hours then sunrise won't help you all that much. If you know his office hours then you can do have to figure out the difference between your time zone and his, apply it properly and you have you're answer. i.e. If you are in Vancouver, or any other West Coast city then you are MST or MDT (UTC-8 or UTC-7 if day light savings has kicked in). So depending on the time of year you are 1 or 2 hours ahead of them. Now quickly, in your head, if it's 12 noon in Vancouver on Oct 1st, what time is it in Regina.
If you were both in UTC and DST is ignored then it's simply, Regina works 15-23 (24 hour clock), I work UTC-17-1, I can call him any time after 16 before 23.
The other issue, which as a computer geek I see more and more, a lot of departments are not working 9-5 anymore so even with timezones I still need to know the working hours of people in my own time zone.
BTW, by my example, it would be either 1 or 2PM in Regina depending on if DST was in effect in Vancouver.
Did you know, that St. John, Newfoundland, Canada has a time zone of UTC-3:30 (yes, 3 hours 30 minutes) and 2:30 during DST.