Now, the criteria is that the site is "dedicated to the theft of US property", but advertising agencies and payment processors are held immune to liability for actions they take under the law, so they have no reason to verify that the site is, in fact, dedicated to theft before shutting it down.
There does not need to be an active government conspiracy for this to harm websites.
There were never claims that the DMCA would literally shutdown sites like youtube and reddit. But the criticisms of it certainly seem justified in hindsight.
The conspiracy theory is that the unintended consequences are in fact intended by the MPAA/RIAA. Given their past and present behavior, it's not a stretch.