If you want live high quality streaming, a lot of reasons bit torrent works so well goes away.
Latency matters. In bit torrent if the peer goes away, no big deal, just try again in 5 minutes with another peer, you are downloading in random order, who cares if one piecs is delayed 5 minutes. In a live stream your app is broken if it cuts out for 5 minutes.
In bit torrent, everyone can divide the work - clients try to download the part of the file the least number of people have, quickly rare parts of the file spread everywhere. In streaming everyone needs the same piece at the same time.
Bit torrent punishes people who dont contribute by deprioritizing sending stuff to peers that freeride. It can do this on the individual level. In a p2p streaming setup, you probably have some peers getting the feed, and then sending it to other peers. The relationship isnt reciperocal so its harder to punish freeriders as you can't at the local level know if the peer you are sending data to is pushing data to the other nodes it is supposed to or not.
I'm sure some of these have work arounds, but they are hard problems that aren't really satisfactorily solved