What's the difference between needing to know what timezone some place is in, vs. needing to know about where their day falls?
What particularly annoys me about timezones is that times are already useless. When does the day start? (And I mean the normal cultural day, not your personal day.) Be it 7am, 8am, 9am, or whatever your answer may be, it sure isn't anything sensible like 0 or 1. If those are anything, that's when the day ends. If the sun rises at 03:00 in one place, 10:00 in another, and 22:00 in another (presumably we'd stop using "am" and "pm" as the a & p would become useless), who really cares? It's not like we're taking away the 00:00 sunrise that you can set your watch by from anybody.