Its pretty hard for PSP to break this reputation at this point.
Thing is, any console which has gotten to that 20 million mark, has probably 100 "good games", in that it has 100 games that are reasonably successful from a design standpoint for what they intend to do.
The real problem is the appeal of the games, as many have said.
I can look on this site and find that there are over 40 DS games which have sold at least 250K copies in Japan alone. And people will say "not all of those are good games." But no one can say they are low-appeal games.
And the games PSP was banking on being high appeal, the games to "bring handheld gaming out of the ghetto," turn out to have mediocre appeal on handhelds, even if they're exceptional titles.
"[Our former customers] are unable to find software which they WANT to play."
"The way to solve this problem lies in how to communicate what kind of games [they CAN play]."
Satoru Iwata, Nintendo President. Only slightly paraphrased.
