Removing time zones would break any kind of cultural joke and reference to time. "omg, i woke up at 4am today!"... Especially in todays internet connected world.
Swatch tried to intruduce timezone-free time many many years ago called "swatch internet time", Ericsson even had it as default on some of their cell phones to promote it. Needless to say it didn't work. http://en.wikipedia.org/wiki/Swatch_Internet_Time