You basically have to reinvent timezones every time you make any kind of calculation involving people in another timezone.
Similarly, you are on holiday and someone tells you a museum is open till 04:30. Can you go to dinner first?
I guess that a main question is what kind of query is more frequent: "What time is it now in X", or "At what time is X where I am now?". I thought the former was way more frequent, but now, I do not know anymore.
Maybe the best thing to do is to drop absolute references altogether. IMO, "Shall we meet in 3 hours" is easier for handling across timezone discussions, and will work equally well for "in a different timezone than the one I am used to".
Of course, your SMS/ping/twitter/email client would have to automatically count down such timers for you.
For someone who travels a lot, a single time zone may well be more inconvenient, hard to say.
Times relative to now would work well but could be unwieldy. How do you do it if you're e-mailing or texting? If you want to meet next Monday afternoon, do you say "in 2 days and 5 hours"?