The thing with this is I just can't imagine the App store getting shut down because of this, or even youtube.
There would be a serious uproar if that happened, people wouldn't stand for it.
More likely is that some pirate sites will die and others will just go deeper underground. The people who are likely to be scared into shutting up shop all together will be smaller distributors of independent or amateur content.
I would be saddened if the Internet became like the high street circa 1996 with a few large companies and producers setting the agenda for what we will watch and listen to.