Not all DS games need to use the screen as a gimmick; while virtually every title makes some use of it, there are a LOT of good games that, in short, only use it for menu-like things, while all the actual gameplay is done on the other screen, in the traditional manner with the pad and buttons. The DS Castlevania games, (excluding Dawn of Sorrow, which technically had a "seal" gimmick) as well as the Mega Man ZX series, come to mind there.
The DS also does have its own footing in jRPGs as well; if memory serves, the DS version of Final Fantasy III happens to have out-sold every normal japanese-style RPG, including every spin-off of Final Fantasy VII that appeared on the platform, like Crysis Core. And additionally, the DS version of Dragon Quest IV on the DS falls between the sales levels of Crysis Core and every other PSP game.
However, it's not to say that I don't think that the PSP is under-respected. I'm just stating that you're giving the incorrect reasons. Rather, What Sony has done impressively here is make a portable machine that wasn't an utter flop in the face of the terrifying monster that is Nintendo, with their 30-year dynasty and nearly a third of a billion units sold. Similarly, especially after additional upgrades to the RAM pool to add another 32MB, makes for a pretty flexible, programmable platform. It's potency, I feel, lies more in as a homebrew and hackable device than an actual gaming platform, which is most likely why it's seen a level of success that was not present for other handhelds that competed with Nintendo's.