You have to remember that the AMD and Intel of today are very different companies than they were 20-25 years ago. AMD split off it's fab capabilities, acquired ATI, adopted TSMC as a fab, and developed a custom silicon business.

At that time AMD wasn't in the custom CPU business, AMD64 was a new unproven ISA, and x86 based CPUs of that time were notoriously hot for a console. These were also some of the reasons why Microsoft moved away from the Pentium III it had used in the original Xbox.

The PS3 was launched in 2006 but the hardware design was decided years earlier to provide a reference platform for the software.