Why did McDonald's invent the McDouble?

The double cheeseburger (2 burgers, 2 slices cheese) on the dollar menu was not making enough profit.

McD took it off the dollar menu, but were greeted by howls of complaint plus lots of desertions to BurgerKing, Wendy's, etc.

McDonalds invented the McDouble as a compromise; 2 burgers, 1 slice cheese, back on the dollar menu.

It seems to have been a partial success; no more howls of complaint, and some customers came back; BUT some people have noticed that Wendy's double stack is still 2+2 rather than 2+1, and is still 99c.