We already have a "World Clock" - you can adopt it too. Just always work by Zulu time.
So if someone asks you what time it is, give them the answer in Zulu time. When they look confused, explain.
Then you'll have to work out what time - Zulu time - you have your breakfast, and your lunch, and your evening meal. So suddenly you'll be having breakfast at, say, 12:00 Zulu. Does that help? How does it help?
So I want to phone you - how do I know what time to call? Any time after breakfast? Cool - what time do you have breakfast?
So, are you instead going to synchronise your day to mine? I sure as heck aren't going to go to bed when the Sun is at its peak and get up a little after it has set. Would you do that?
This comes up every year or so on HN and I honestly just don't understand the mind-set of people who suggest it. I'd seriously like to know how you would address the above, and how you can see this possibly working.