If you schedule a meeting at 13:00 UTC, is the Chinese guy still in his office? Is the one from the US already in his office? Instead of knowing their timezones and their offset you'll now have to know their office hours in UTC, which means things keep being just as complicated as they were before.
But what if it's not a scheduled meeting? If it's the middle of the day where I am, and I need to give you a quick call to verify something, I need to figure out if it's appropriate to call and if you're likely to be in the office.
Currently, that means converting my time to your time, as easy as looking up the offsets and doing a simple sum. Context clues make it easy to figure things out: if it's 10:30am your time, there's a high chance that you'll be in the office. If it's 3:30am your time, you're probably asleep. Sure, there are still cultural fudge factors at play (do you come into the office late, do you take a siesta, etc), but a ballpark estimate isn't hard. Assuming it's not an emergency, I don't care if I get your answering machine if you're in a meeting; I do care if you're offended that I woke you up.
If we're both operating in UTC time, this conversion now requires cultural knowledge of what your working hours are before I can even get a big-picture idea of whether it's appropriate to call.
I know that my partners/customers/colleagues in all countries are available for calls from roughly 9:00 AM to 5:00 PM without ever having to ask them.
That's basically what TimeZones do for you - they provide a common basis to keep everyone in sync around with world, without me having to check, on an office-by-office basis what UTC hours they are in. It's just agreed that 9:00 - 5:00 is a reasonable time to schedule a meeting, and TimeZones tell me when 9:00 - 5:00 is for any particular office.
I don't work (yet) with anyone in China, so I can't comment on that country.
Report back in a year on your results.
