You can still have McDonald's Tokyo open at a different time than McDonald's London. Just have everyone label their opening and closing times in UTC and be done with it.
"I'm in Berlin, my working hours are 7:00 UTC to 15:00 UTC, and I'll be reachable until 20:00 UTC".
Arguably, without timezones, it's much harder to figure out when its daylight in a particular region, so when someone should be reachable.
"Well it's 06:40 UTC, but what time does the sun rise in New York? Has the sun set in Bangkok?". Meanwhile having googled that it's 02:40 AM in NY means I can be assume a normal-working person would be asleep at this time.
If you know someone in a different time zone the first thing you establish is when it's ok to call. Nobody cares about sunlight. There are more important things like when do they work, when do they get home etc.
Perhaps that's cultural. Most people in my social circles care quite a bit about sunlight. At home, the evening routines that we do with our children are based on a combination of season and sunrise/sunset. I find it somewhat surprising in fact that this is not at least partly the case for others, excepting of course people that work 3-11 or 11-7 or what have you.
I didn't mean people don't care about sunlight in general, of course they do. Just that people don't consider it when phoning someone in a different time zone. If I'm contacting someone in a different time zone I just think "It's before 11:00 so I can ring them" not "it's daylight there so I can/cannot ring them".
