How would that help? Timezones help to coordinate hours with day and night. If you know something happended somewhere at 3a.m. you can assume it was night (unless it was a polar day). Without timezones the task becomes much more difficult.
If I'm in New York following the nuclear crisis in Japan, it's probably more important for me to know that the next news conference is two hours from now than that it's in "the morning" there. If I'm planning a meeting I certainly want to know the absolute time it's occurring, and only care about the relative time depending on how courteous I am.
I'm not saying we should stop caring about working hours and daylight hours in various places. I'm just saying that those vary wildly and are dynamic, and we should reflect that in our concept of "time".