For some emulators, it’s not worth it.
The PSP has low system resources for this to begin with.
It’s mainly a memory issue – 16MB main system RAM is not a lot to work with and some emulators require more than that to run smoothly.
Everything also has to run off the Memory Card. A faster card helps but transfer speed will be a limiting factor for the EMU, too.
Also, I have read of people getting arcade fighters to work on the PSP but consider this…
a) you have to find an emulator that works with the PSP IF you have a cracked version of the firmware;
b) the emulator probably will not run at full speed because of the RAM issue; the ROM of the game plus the size of the emulator might be a bit too much for the PSP; MAME and most emulators only run well on personal computers because of RAM issues. A processor over 200MHz generally works well for a good chunk of the games ever programmed but if you don’t have the RAM to run the emulator smoothly…!
c) the PSP is horribly set up for fighting games… Bad d-pad, insufficient buttons and bad button layout for 6-buttoon fighters; and
d) when I owned a PSP I did have the occasional system lock-up/crash with emulators. It mainly happened with Doom!