That would require a drastic change in law. Right now, you're not responsible for the illegal distribution of things you own if they're stolen from you; that phrasing doesn't seem to have an allowance for "college roommate hacked into my computer and copied all the files."
There's also the issue of defining "personally responsible." How do you prosecute someone who *didn't do the act* but is somehow "responsible?" Does that mean the person who did the distributing is off the hook entirely--that if you get an unwitting permission from someone to "borrow some books to read," and then load them to the torrents and fileshare sites, they, not you, are guilty of copyright infringement?
And "absence of personal ID by the owner" is also hard to prove. What counts as ID? If I knew it was downloaded by DragonBane381, R33DERG33K, and Fan-of-ebooks, does that count as personally identifying them?