BitTorrent doesn't order file fragments by design. So how can you stream it without downloading the whole thing first (to the server at least)? Which defeats the purpose of streaming really.
You can. BitTorrent doesn't order file fragments by design, but clients can choose to ignore this and request pieces in order. See Popcorn time and many other implementations out there.
Why don't the other clients in the swarm penalize the client for this behaviour? Downloading all the fragments in order means that if the initial uploader drops off, everyone is stuck.
It kinda works here because the shared files are already very popular, and there's a lot of seeders (ie peers who have 100% of the file and can share any part).