It would be a mess talking to anyone about time where you do not live.
Say that you wake up at 06:00, everyone understands. Remove all time zones and now you wake up at 14:53. Anyone not native to your location would have no clue where in the sky the sun is relative to you and what that actually means for your day.
Would 14:53 for you post removal be compared to 06:00 or 09:00 pre removal? What if oyu are porned post removal and do not have the frame of reference for the old system. How would you go about it then?