On the plus side, people can pick the point at which the day changes. For example, 1am Thursday is really an extension of Wednesday night for most people.
On the minus side, the time becomes required for meaningful conversation. In your system, saying "Let's get together Tuesday" would be ambiguous. People have a sense of what a day is, and what day it is. Messing with that will lead to... unintended consequences.
> qntm.org/abolish
Yeah, I've seen that. My idea would hopefully solve the day-related problems (days changing at midnight); otherwise, it would require changing our way of thinking about things from "What time is it there?" to "What time do they work/eat meals/go to bed/etc. there?"
> On the minus side, the time becomes required for meaningful conversation.
Not necessarily. People close to each other in longitude would probably tend to be in the same day during the day, differing mostly during the night, except perhaps people who work night shifts or are otherwise nocturnal. People in different parts of the world will be in different days, but that's not any different than it is now.
> People close to each other in longitude would probably tend to be in the same day during the day, differing mostly during the night...
Differing during the night is... significant. Also anything written will be stripped of the needed context, leading to ambiguity later (if not also sooner)
> People in different parts of the world will be in different days, but that's not any different than it is now.
It is different from now, because at least now we know what day they are in wrt the day we're in. If everyone gets to define their own day, all bets are off.
Tuesday isn't Tuesday anymore.