Your travel examples are indeed more difficult, but I travel much less than I coordinate times across time zones, and I suspect most other people do as well, even if it's something as simple as calling family in another state.
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"?