Actually, there is another way of dealing with this. Specifically you can drop any attempt to enforce copyright among private individuals, avoiding any entanglements with their moral rights, and restrict the application of the law to incorporated entities, which have no moral rights.

That would mean private people could do literally anything they like with digital media, making money included. But it would also mean that any commercial operation that got big enough to warrant incorporating would be exposed to crushing penalties if they knowingly and willingly violated the copyrights of others in the course of doing business.

It's one thing for a kid to know nothing about copyright, to care less, and to be free from the burden of compliance with law that was never intended to govern the private conduct of individuals. However, if you're doing real business and copyright protected material is helping your bottom line, then you need to comply with the law and help cover the cost. This is actually how much of the copyright protected world operated before the internet, so as a practical matter, the means to manage this risk are already well-developed, reflected in law, and supported by precedent.

In practice, this would mean that clients of ad networks would need to know their vendors, or risk lawsuits stemming from business done with shady players. For instance, if a site owned by an incorporated entity is serving pirated content to attract the traffic it sells inventory against, we're no longer talking about people swapping hard drives in their dorm rooms. We're talking about large, publicly-facing companies paying the bills of pirates and getting commercial advantage in return. Presently, the content creators at the heart of this trade get nothing. What they really need is to be able to sue those fuckers into oblivion - networks AND advertisers.

Again, this isn't an unprecedented situation. Broadcast networks have always been liable for infringing material they air. That's why they always require producers to both certify that they have the rights to everything they're selling to the broadcasters, and carry Errors & Omissions insurance that indemnifies broadcasters in the event that some clearances were missed. (Unlike patent trolls, copyright trolls can be insured against). A producer with too many insurance claims against him will get dropped by his underwriter, rendering his work commercially untouchable. This is a mature and well worked out system, not a theoretical approach.

An extension of this system into the ad-supported space would make advertisers (who ultimately pay for everything) liable in cases where their ads run on dicey networks and sites. That would make E&O a mandatory part of running a site, and place the burden for securing clearances on any commercial distributors of content. You want to host User Generated Content? Super, feel free. You want to sell ads against it? Watch out.

The real point is that people who say "there's no way of dealing with this" are not correct. They are simply reflecting their own lack of knowledge, curiosity, and imagination, along with total indifference to the legitimate and unavoidable economic needs of the content creators who remain a vital part of any attention-based ecosystem.