Because x86 is past it's sell by date?
Im no expect in either architecture but if i had to guess i put it down to performace.
Performance may be 1 issue, depending on what sort of performance you are looking at. I am sure there are many, many areas where a chip like Core2Duo mops the floor many times over compared to a chip like Xenon. But Xenon gots the nice marketing flops and from browsing the MS patents it seems one of the ideas behind Xenon was doing a but of graphic work on the CPU, and that is where the beefy VMX units, Dot product output, cache locking and datastreaming from cache to the GPU come to play. Not that MS chose Xenon to begin with, they actually wanted an OOOe CPU.
Anyhow, I think the major reasons are
(1) IP licensing. MS wanted more control over the IP, both for backwards compatibility purposes as well as for future process shrinks and possible system wide integration (e.g. GPU and CPU on a single die). Intel and AMD have little reason to make such concessions to MS. MS also wants control over the IP so it isn't fixated on one fab partner. They can dangle the contract to TSMC or Charter and so forth and get the best deal. If MS went with Intel it would have been locked in with Intel for pricing.
(2) Intel and AMD are very tapped in regards to fab supply/demand. They sell all they can make. It costs Intel and AMD ~$40 to make a CPU. They in turn sell these to mass wholesale retailers anywhere from $150 to $1000. Considering they are binning their chips (best chips are sorted as $1000 CPUs, chips that hit lower frequencies become the $150 chips, and everywhere inbetween) they make a HUGE amount of profit. They have a lot of R&D, fab maintenance, marketing, etc to pay, but that $1000 processor cost them $40 to make. On the console side MS would want to give them razor thin markup -- probably much less than the 30-40% markup GPU makers make. Considering the very high end of Xbox 360 projected sales would be 60M units in 5-6 years they are looking at 10M units at very low margins. Intel and AMD ship about 200M PCs a year at high margins. As a business, do you cut out the 10M high profit PC chips for 10M low profit console chips?
That said, I believe Gates had lobbied for Intel a bit. If MS could have got an X2 or C2D in the 360... boy, we would be having a lot of fun debates right now
Instead MS kind of got screwed. We hear some complaints from PC devs about Cell, but you don't ever hear, "But boy, that Xenon, what a dreamy chip!" hehe If MS had an X2 or C2D in there I am sure we would be hearing a lot of praise, especially from the PC devs.