Anyone who has a PSP laying around somewhere should go have a look at it because the battery in them consistently turn into a rather spicy pillow. Which I guess makes mod like this more interesting.

Awesome! It looks like eBay still has relatively inexpensive units sold for parts, so you can avoid cannibalizing a working PSP-1000 for this. I wonder what it would take to adapt the design for the smaller PSP-2000/3000.

it's an interesting idea for sure but there's always been a plethora of homebrew emulators for the PSP. do they not work well anymore? Or does the Pi just have more modern emulator options?

A fine one-off.

Pi SoCs have no sleep/suspend mode, so you'll be pocketing it powered on or waiting for it to boot every time you go to use it. Furthermore, you have to destroy a PSP to build this, AND buy an overpriced Pi (seriously, go look at the prices now) to shove in it, which will probably cost you more than a more capable and already-built modern retro portable.

All that aside, I have been down such paths enough times to know that this stuff is drawer filler within 3 evenings. People killing vintage hardware to build "cyberdecks" that are basically unusable and will just end up in the dump soon after is just the latest atrocity along the path to hell. Do what you will.