That has it's own issues. Either you need some people to wake up in the middle of the night because it's now "morning", which would destroy people, or you need a way to figure out what part of their day night cycle people are in, which is what a time zone is.
The difficulty isn't because of the maps, it's because humans evolved to care about day-night cycles, being round, the earth has a continuous day night cycle, and it's only recently that we could suddenly talk to people in drastically different places. There's just no way to reconcile them.