Why do you need a timezone for that? You can consult a table of normal working hours for that region and select a time from that. Or ask them. It's still more efficient than using a time zone because the exact time is shared by both parties. It's not "have it done at noon your time, eight o'clock my time", which is what we currently have.
People that work across different time zones need to utilize UTC better. But we already have it. It's called Universal Time. But this isn't about that. That's not what most people use the clock for.
I don't get it. If you follow the clock this is even easier. If in the past 8:00pm was decided to fall on the moment the sun rises would you be following that paradigm right now? Or would you still need your clock to be set as it is now? If went into your house and changed your clocks by five hours, and you knew they were different by five hours, would you suddenly be unable to function?
This has nothing to do with "it's just arbitrary". Let me explain this once again:
We implement Universal Time. Boom. Done. You now live by a clock where the hours are as arbitrary as always. You get up at 14:00, and you go to sleep at 4:00. You eat lunch at 17:00, and you work out at 23:00. You're right. We'd all get used to this.
You're going on vacation. Hooray, this is the time you've been waiting for. You no longer have to set your time zone! It'll be universal! Yay! So you're there. You land at 20:00. You think, great, I usually eat at 22:00, so I can get to your hotel. It's a really grey day out, and the lighting is really flat. You have no clue what time of day it is. Instead of eating, you fall asleep when you get to the hotel.
You wake up at 11:00. You think to yourself that that's really early. You look at the window and see that it's dark out. Then you have to start thinking. "Ok, I looked up that Tokyo is -7 hours from my place. That means that 11:00.. that's.. 4:00. Wait. It's.. It's really late! (You're on a +5 hour different so the clock you have now, so that means 4:00 - 5 = 23:00. It's 11 in the night.)
You now have to translate every single time when you're out traveling for it to make sense to "what time it actually is". You're right that you'd get used to the new clock at your place, but the issue is when you travel outside of that.
You even try to use UTC as a good way to work across time zones. You're now assuming everyone's awake at the hours you are, which they aren't, since we're still following our circadian rhythm. Now you have no idea what time it is to someone else. You know that it's 14:00 UTC, but you don't know if that's late or early for someone in Europe. Our clocks are relative to the sun, and this is why.
What time does the meeting start? 11:00am.
You have participants in the meeting in five different time zones. What's easier? Everyone dials in to the meeting at the time on their watch, or everyone does math to match that time to their local time zone?
Do you often wonder what people half way across the world are doing at a certain time for no reason?
There are so few people that do this. 95% of people never have to deal with these things on a daily basis, and we already have the fucking UTC for this exact purpose. It just means that you can lookup what time it is in Tokyo and realize if you're asking people to be up in the middle of the night or not. Not having a relative time makes no sense.
Oh god yes. Time zones and leap years
This has nothing to do with leap years or even leap seconds. This doesn't change the problem with representing time, and programs use epoch time, anyway. As a programmer, this doesn't solve that much, really.
