"readjusted their schedules" is such a ridiculous hand-waving away of serious problems with the idea.
One of the biggest problems is that weekdays completely cease to make sense. With timezones, the day of the week changes at midnight, when most people are asleep. You wake up in the morning, it's a new weekday, and it's the same weekday for as long as the sun is in the sky.
If we abolish timezones and choose UTC as the one time, the day of the week will change at 5pm in San Francisco. Say that you have an establishment that is normally closed on Sundays. It's 4pm on a Saturday, do you close in an hour because it is then Sunday? Or do you change your "schedule" so that your establishment is closed on SundayMondays instead? Or perhaps you keep it closed on SaturdaySundays? Because the concept of "Sunday" doesn't make sense anymore, "Sunday" is no longer a contiguous period of normal waking hours.
In San Francisco. In London it's business as usual. But in Sydney the day of the week changes at 10am. When is "Sunday morning"? 9am Sunday morning is the day after 10am Sunday morning. Every week has two Sunday mornings now. (And two Monday mornings!) Which one of them did you mean?
Adjusting computer systems is much, much simpler than getting humans to accept this idiotic system.