well, psp was the console with most homebrew and cool stuff... with a true custom firmware, it was the wonders of homebrew....
however, after the psp, android become famous, since its open source and almost every phone has it now.. portable console homebrew become kinda irrelevant...
the psp had homebrew for lots of functions... there was homebrew games, calculators, tools, calendars, file managers, readers.. emulators, even chat like msn.. there was a bit of everything...
but now with android devices.. there is no great use of console homebrew, its still cool, but now an android phone can do everything that a portable can do.. whats left on consoles like psp is rom\iso loading... so that you can play the games designed for that system...
in the past i used my psp for lots of stuff, i even used it as a calculator in school, or to read e-books, music etc..
but now i only would use it to play pirated psp games.. but its still a great emulator anyway...
and i can just got a gamepad that attaches to the phone if i don' like to play using a touchscreen on the phone..
and as a developer side.. there is no really a reason to develop stuff for a console anymore.. of course you can still translate games and modify, but for homebrew there is no great reason, android is open source and much more easy to develop and share...
the only reason to develop to a console is the "trill" about unsigned\foreign code, its the feeling about you doing something that is kinda forbidden... and in case you don't have a buck to buy a cheap ass phone.. or because you just feel like to...
psp huge success was thankfully to being a portable device (that was kinda easily to hack and to develop to) and because android was not a thing...