Ooops, that's a good point. I suspect that the whole DMCA safe harbour "we honour all correctly submitted takedown requests" is a bit of a get-out for a lot of these sites. Especially the ones that are pretty much basing their entire business model on access to pirated content.
At the same time, there are legitimate indexing & hosting services who probably are genuinely displeased with the abuse of their systems. The same problem as the homebrew console hackers often enabling subsequent game piracy.
The tricky part is how to tell them apart, and what the legitimate concerns can do to prevent abuse, and the content rights-holders can do to deal with the bad-faith lot.
Providing the value/product that consumers are looking for as well is another big deal - from what little I know of mobile app-stores, the low-friction discovery/payment/install process, along with low-cost high volume business models is reducing piracy to some extent. Contrast with music, where DRM, onerous formats, and unavailability of a lot of content is encouraging or even forcing people to go the illegitimate route.