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.
So you're effectively substituting one form of synchronization for another that's already well established. After all, we already go to the trouble of using DST as a way to better synchronize within a timezone. (Which not everyone likes but I appreciate as a resident very far east in a timezone.)
