Why three cores? I'm not sure – but today they announced that they will be adding triple-core Phenom processors to their roadmap for the near future. In a video posted to AMD's site, they pitched it as a CPU that gave a competitive edge in various markets, from desktops to enterprise. Their assertion is that quad-core and beyond are giving diminishing returns, particularly in the desktop market. Obviously, this means a price reduction between these CPUs and another quad-core variant of the same series.
It is a short video, and has more marketing speak than actual technical justifications, but is interesting nevertheless. Depending on the price different between dual, quad and now triple core processors, maybe they will have a fit on the desktop.