That’s a problem I already have, because I can never remember what time zone people or places are in. On the other hand, with a single time zone, there is never any ambiguity about what time someone/something is referring to (Eastern or Western? DST or non-DST? Etc)
You still have to remember where people live. Just because it's 9am everywhere doesn't mean people on he opposite side of the globe will work through the night.
That's already a solved case: communicate using UTC times when dealing with people in other timezones. It then becomes their responsibility to know their time relative to UTC. There are even sites that you can set a clock for a specific UTC time and when people visit the URL it will use their local time so they don't even need to deal with converting to/from UTC at all - technology does it for them.