I don't buy this line of reasoning at all. The idea that a company large enough to have offices in multiple timezones would make a single blanket statement about work hours to all of its employees worldwide is preposterous and bizarre, like something out of a badly-written episode of Dr. Who. The way such things actually work in the real world is, a given employee's immediate supervisor tells him what time he's expected to be at work. If the numbers given to an employee in Chicago are different from the numbers given to an employee in London, nobody would even notice much less care.

The larger problem with switching away from timezones is the mere fact that it's a change from the current system.

As with any deliberate society-wide change, people who aren't so bright (of which there are many) would have a hard time getting the old system out of their heads and learning to use the new one (UTC presumably). It could be done, but it would be difficult on approximately the same order as switching to metric. (The benefits would be much greater than for switching to metric, but, unlike with that switch, individual countries would not be able to receive the benefit from switching unless everyone else, or at least most everyone else that mattered, switched too.)