It's not just meetings, it's everything. Let's say you run a chain of stores that you all want to be open the same relative times. How do you list the hours on your website? With time zones this is easy, you just say "all stores open 8am to 9pm M-F", or what-have-you. Without time zones you have to specify the UTC time for each store or for each region. E.g. Stores in California open from 16 to 05 UTC, stores in Texas open... And now you see another problem, because now a time during the day locally is running over into night. So how do you specify the hours you are open relative to the days of the week? Are we using local days of the week or UTC days? So now if you are closed on the weekends locally that translates to the last day being open on Friday/Saturday (UTC).

Now let's say you want to buy a ticket for an international flight. You're only going to be staying for a few days so you need to plan the time of day you leave and arrive carefully. For example, let's say you want to fly somewhere for the weekend, you want to leave in the evening on Friday and begin your return in the evening on Sunday. Now you need to translate between UTC and local time and days to figure out which flights you want to take. Or, say you are taking a very long trip, from the US to Australia perhaps, and you want to arrive in the evening so you can eat dinner then go directly to bed. That too requires complex figuring if you don't have time zones.

Or, let's say you are a service oriented company and need to provide a response-time in your SLA, measured in business days. Well, do you have to introduce the idea of "local business days" now? How do you list local holidays? "Offices closed from 08 UTC Dec 25 through 08 UTC Dec 26"?

Ultimately you end up needing to have some sort of additional resource which tells you things like the local time, the local day of the week, etc. And that merely duplicates all the work we've already done with time zones. If you want to simplify time zones, that's a worthy effort, but getting rid of them is not the answer.

If we all operated in UTC time, you would probably very quickly get a feel for when other people are at work. I'm on the east coast, and when working with people on the west coast I often just imagine them as working 12pm-9pm.

Trying to remember the hours people work in Japan may be a problem, but I don't think it's any worse than trying to remember timezone conversions and I don't think it's a large enough problem to warrant varying the way people measure time. It may have made sense at the time, but today it is vastly overkill. That said, I doubt it will change anytime soon due to inertia.

If we're just wanting to know what phase of the day it is, at a particular location, a sun projection is a good enough approximation.

e.g. http://www.die.net/earth/

So, the one case gets way easier; the other gets no harder. Seems like an improvement to me.