Commercialization of the streaming video via P2P is evidently still in its early stages. A google search for “P2P video on demand” returns only one advertisement at this time, for Kontiki, Inc. (Kontiki, 2010). And their technology appears to be fairly LAN-centric. Such a search does, however, return numerous links for research and development so it is probably safe to assume that we will see the paradigm catch on unless some patent(s) stifle(s) it. It is hard to imagine how the technology could be nearly as straightforward as simple file sharing P2Ps since streaming obviously requires some contiguous chunks but looking at Kontiki's product and all the R&D going on makes one hopeful both that the problem has been solved and that it might be solved in more than one way. Because it makes a lot of sense to deliver such a bandwidth heavy data stream from as close to the receiver as possible and from multiple sources if possible.
In 2005 Annapurredy et al noted that “while a lot of effort has been put in optimizing the distribution of large video files using P2P swarming techniques, little research has been done on how to ensure a small start-up time and a sustainable playback rate”. At least one project has since been commercialized, but it seems the field isn't exactly rife with competition as of yet. Whether this points to continuing difficulties in the field or whether it simply indicates a laissez faire attitude on the parts of users, for whom waiting until the download is complete is an acceptable part of using P2P for media, is a little hard to say.
Kontiki (2010) Video Communication Everywhere [Online]. Available from: http://www.kontiki.com/ (Accessed 17 October, 2010)
Annapurredy, S., Gkantsidis, C., Rodriguez, P. & Massouulie, L. (2005) Providing Video-on-Demand using Peer-to-Peer Networks [Online]. Available from: http://www.scs.stanford.edu/reddy/research/redcarpet/redcarpet.pdf (Accessed 17 October, 2010)