PPC cores, yes. But, they are custom hardware that is most definately off-limits to mere mortals, unless you want to pay license fees up the wazoo through huge contracts Amiga cannot afford. Consoles also don't need certain features reserved for "real" computers.
Note: Most console SDKs don't actually run on the console hardware. They run on workstations that produce code that eventually runs on debug units. I suppose console developers regularly moan about the lack of "custom" hardware in their workstations.
You're quite right that console SDKs run on a seperate workstation, usually PC. We just compile to another target using a compiler supplied as part of the SDK. However thats not to say that you have to do it that way.
The analogy would be writing a demo on an Amiga that when run kills workbench and just bangs the hardware directly to achieve maximum resources and speed.
You could run an OS on a console that built apps for itself using the SDK and did the same. It's simply that the console manufacturer doesn't want you too.
Andy
