I frequently host conference calls with people from other parts of the world. Every time I schedule them it takes something like two minutes for me to check the local time for everyone. It's a minor inconvenience, sure, but nothing I can't manage, it's just a matter looking it up. Same thing goes for traveling across time zones - I mean, you have to buy tickets, wait in line to check in the baggage, wait in line for the security check, wait for the gate to open, sit on a plane for several hours, and then to everything again in reverse order on your destination. Adjusting your clock, on the other hand, only takes a few seconds to do.
Time zones are good. They were invented for a reason, and those reasons still stand. In fact, in China where the whole country runs on the same time for political reasons, the Western parts of the country has adopted an unofficial local time that better matches the sun's movement.