Extend the issue out, when I want to call my mother around the world, how do I know she's not ill today, took the day off and went to bed early?
You're creating an issue by extending something to absurdity.
Specifics like that aren't going to be communicated with any system, but removing timezones removes the general idea that is communicated with 9am or 7pm.
Siesta is an essential part of daily schedule in many places. “Took the day off”, “ill”, “went to bed early” are obviously extraordinary circumstances.
Because instead of just remembering that Spanish people siesta from 1200-1400 local time, you might as well translate it to UTC and make it even more complicated to remember?
It is possible that it appears complicated because it is not common to use UTC. But let's try to imagine the scenario further...
So Spanish people typically siesta between 1100 to 1300 UTC. Imagine, my home country is UK. I work between 0900 to 1800 UTC. Imagine I travel to US and need to call my Spanish friend. In the US, when I reach the east-coast I realize that I work between 0200 to 1100 UTC. At once I can deduce when to call my Spanish friend; it is before I leave my work at 1100 UTC.
Frankly, even I had not thought through completely the UTC based scenario, until now. I am now even more convinced that it's the most convenient way forward.
When does your Argentine friend siesta? When does your Japanese friend get off work? What's a good time to phone your friend in Australia? You've just landed in Tokyo--when should you be getting to sleep? You still have to do time zone calculations, but you don't have the time zones anymore.
9am is the morning everywhere in a time zone, 3 hours before noon when the sun is highest and the work day ends at 5~6pm. Seasons don't matter here.
"What time is it in Sao Paulo?" "7pm" "Damn they've gone home for the day." Whether it is winter or summer, that doesn't change this.