Timezones make it so that daytime is "almost" the same for people in relative proximity. "Today" is almost the same timeframe for most people who are awake at the same time, regardless of their location, give or take a couple of hours. While long distance communication tools have somewhat eroded this notion, it's still true for the vast majority of interactions. If you switched everybody to UTC, the international date line would result in massive confusion unless all times are augmented by the date for reference. Besides, switching to a singe timezone doesn't solve any significant problem.
Um, if everyone were on UTC, there would be NO "international date line".
Which would remove TONS of confusion.
The biggest problem for people would be that the date would change in the middle of the day for a large number of people. Your work week might be from 2200 on Sunday to 0800 on Friday, with a date change 2 hours into each of your shifts.
It would also be inconvenient for anything which is normally advertised as a date range, because times would have to be included with the dates.