I am pretty sure everyone's office hours (to take it as an example) are still going to be fixed at, say, -4 hours back from their noon till +5 hours forward, so instead of saying "UTC+4" people are going to need to learn to say "my noon is at 16:13" (or "16:00" even, i'm pretty sure no one will want to live by any offset from the "global" noon other than those evenly divisible by 30 minutes). Probably abolishing timezones is much less of a profound change than it seems to be.