Comparing HTTP Live Streaming to P2P video streaming over UDP/RTP is almost like comparing apples and oranges. More like oranges and tangerines... read on.
HTTP Live Streaming was designed as client-server protocol without P2P or NAT traversal consideration. The idea being that the streaming server is already over HTTP/TCP and accessible from the public internet as if it was just an ordinary web server. The key features of HLS is its ability to dynamically switch the bitrate based on how well the client receives the stream. If the client connection to the server hiccups trying to stream down a 1080p video, it can transparently switch to sending a lower bitrate video (and likely switch back to streaming at higher bitrate if network conditions improve). Good example: Netflix.
WebRTC and ICE were designed to stream real time video bidirectionally between devices that might both behind NATs. As such, traversing a NAT through UDP is much easier than TCP. UDP lends itself to real-time (less latency) than TCP. Most video-chat clients (ala Skype) have dynamic bandwidth adjustments built in to their codecs and protocols to achieve something similar to what HLS does.
I suppose you could combine TCP NAT traveral and HLS together. Doing HLS over UDP implies that you build a TCP like reliability layer on top of your UDP stream.
Hope this helps