What killed it is all the games were watered down versions of console games. PSP games were really unsatisfying on average, for no obvious reason. I own one with a bunch of games, and tried (hard) to really scratch the gaming itch when I was traveling for work all the time with it. I gave up and started lugging an Xbox 360 with me sometimes... The game to date I've played most on PSP is the PS1 version of FF7 (which I bought from the Playstation store, fwiw).
The DS had way more piracy and was a runaway success by all accounts.
Consider this: Nintendo has a history of understanding what gamers really enjoy; Sony has a very inconsistent history of this.
Read these two articles from the perspective of Sony selling ~83 million PSP's, and Nintendo selling ~154 million DS's:
https://en.wikipedia.org/wiki/List_of_best-selling_PlayStati...
https://en.wikipedia.org/wiki/List_of_best-selling_Nintendo_...
Getting back to my argument...
If Microsoft could figure out how to make a profitable Xbox One portable at a 300-400 dollar price point, make it digital-only (maybe with some option to import a game off a disc from your console), they'd sell a gajillion units.
My dream of a portable game console is playing Left4Dead for hours on end stuck in an airport. Still not doable - thanks to limited battery life of the Steamdeck-like portables.