I own a PSP (actually 2 -- I have a 2000 and a Go) because its a great game system and I own about 40 games for it, but I know several people who own a whopping 2 games, and use it mostly as a MP3/MP4 player and portable web browser. I know this is anecdotal, but I think this is actually pretty common -- and the numbers certainly seem to support that hypothesis.
Also, unlike home consoles, handhelds (like the PSP) are usually sold for profit by the manufacturer.
Since the PSP is part music player, part portable video player, part game system, you can't call it a "failure" because it doesn't sell *game software*. That's like calling a company's MP3 line a "failure", because it doesn't sell proprietary music, or it'd be like calling the iTouch a failure, because the Apple store's games revenue is far far exceeded by iTunes revenue.
