I haven't looked at the PSP dev-kits. I'm guessing (legal issues and money aside) we could write an engine that ran under the PSP, but it would require a major rewrite of the core elements (sound, 3d, input, memory management, etc.).

The PSP is a powerhouse of a handheld, but it is still limited compared to a modern PC or console. Normally you are better off writing something from scratch then trying to port over.