Here is another problem. They would likely still need to run some of their own streaming servers. Most of us who watch Netflix probably don't do it on a computer. Two other big streaming services I know of that use P2P are Spotify and Vudu. Both of those services only use you as an upload server if you use your computer to do the streaming. As far as I know they haven't figured out how to turn devices like an Apple TV, Roku, or game console into an upload server. This means that all those people using a computer would be uploading tons of data while those of us using a streaming box wouldn't be uploading any. They probably wouldn't be able to meet all the streaming demand using only people who watch Netflix on a computer as their servers.
Gaming consoles have pretty large internal storage these days but devices like the Apple TV and Roku have practically none. Even in the case of gaming consoles I don't see Sony or Microsoft letting Netflix take hardware resources away from gaming to upload files.