Correct me if I'm wrong, because I didn't really follow the handheld wars, but I think there were a lot more factors involved in the DS' success over the PSP other than just "people saw the innovation".
I think there's a lot of retrospective thinking here. From what I remember, one of the reasons people thought the PSP was going to topple the DS was because it seemed to have a lot more going for it. Heck, when the PSP launched it had more games than the DS had managed to collect in its several month head start. It was more advanced,with a huge screen, and major developer backing. What killed the PSP was all that extra functionality making it cost more than people wanted to pay for a handheld. Honestly, if PSP had sacrificed some of the bells and whistles in order to price the PSP more competitively, it would definitely be a bigger threat to the DS than it is now.
It's easy to say now that the DS creamed the PSP from day 1, but at the beginning nobody was certain. With the DS starting out so slow, everyone thought the PSP looked like a real threat, and for good reason. The DS was less powerful and had less games, and with the touch screen not being put to good use yet the only real benefit the DS had was its price. Luckily, that was more than enough to give it an edge. The DS' and Wii's success are very much similar: they're owed not only to their own design, but also to Sony just royally screwing up and making it easier for them to pull ahead.