The thing with PVR chips is that it kind of does that for you already (Tiles get output one by one to memory, and I think it's possible to set the target format for that too).
I agree you can still break things, or make them slow for some stuff (like ping-ponging render-targets), but that could be special case hacks

I don't think PSP framebuffer operation magic was nearly as common as on PS2.
And as it is, they probably have to hack things for games like those that expect to manipulate Z buffer directly etc, there's no way this emulator was just directly mapped to hw rendering.