>I agree that this reduces wages of high income workers. That's exactly why it reduces income inequality.

The majority of the money saved from those wages would be transferred to the managerial classes (execs, etc.) and shareholders, making income inequality worse:

http://www.forbes.com/2004/08/31/cx_da_0831topnews.html

Income inequality isn't high because people who work for a living are earning too much.