It _would_ be a perfect setup (much much better than sending the same stream through the same lines just because 2 persons are watching the same show)
The problem here is not technical (Bittorrent solves that) the problem is societal: for most of the content that is of interest to population, you are not allowed to redistribute it. So Netflix has to DRM-protect the content for everyone, meaning that the actual content that transits on the line has to be different, meaning that you can't redistribute it (since it's targeted to you, no one else could decode it).
If you want to see how much the technical side works, take a look at PopcornTime.
As I wrote that comment, BitTorrent came to mind with all the societal implications that carries (that's what I meant by "sanctioned" in the last sentence)
I haven't really explored PopCorn Time but I'll take a look.
With regards to DRM, the content must be de-protected before you watch it - so if Netflix installed a mini-box on my network, they could decrypt it to let me watch the show, and encrypt it to store on the device before it is sent to someone else. The key itself could be retrieved from the a centralized server.
If I think about it some more, there really is no need to keep an entire Netflix catalog in every location. As I mentioned, they have usage data and a strong prediction system too, so predicting the next show that will be watched in an area and even when would be "straight-forward" (In quotes because it wouldn't be easy for me to do it, but I think it would be easy for Netflix).
Another thing Netflix could try is pre-fetching shows during off-hours. That would work well for binge show watchers, and reduce peak time traffic.
It _would_ be a perfect setup (much much better than sending the same stream through the same lines just because 2 persons are watching the same show)
The problem here is not technical (Bittorrent solves that) the problem is societal: for most of the content that is of interest to population, you are not allowed to redistribute it. So Netflix has to DRM-protect the content for everyone, meaning that the actual content that transits on the line has to be different, meaning that you can't redistribute it (since it's targeted to you, no one else could decode it).
If you want to see how much the technical side works, take a look at PopcornTime.