The problem with this is that you could get a network of 1000s of households/users and still rarely have clashes in use. Such clashes could be managed such that additional copies are purchased (or the user chooses an alternative item of media) as needed. Then you're probably going to be able to serve 10s of thousands in a group and still reduce overall number of media items purchased.
That's the halfway point between torrent style file sharing and library lending. Imagine you could access the currently used media libraries of all your friends (and "friends") ...
Similarly, I can borrow a book from a public library and make digital copies of it and distribute it. In fact some illegal copies of ebooks you find on file sharing sites are scanned copies of legitimately acquired physical copies (I have personally come across comics with library seals in one of the scanned pirated digital copies). Some pirates also distribute colored xerox copies of physical copies acquired from libraries.
The only difference between the two is time taken to do it.