Advantage of HLS/HDS over direct bytestream I've been becoming familiar with a lot of streaming protocols in the past few years, but now that I ask myself, I don't know what are the advantages of protocols such as HLS or HDS which chunk the stream compared to a direct-from-memory bytestream like HTTP octet-stream, RTMP or RTSP can do for example.

I would think that the I/O necessary to produce the fragments makes it less efficient and, for HLS, TCP already insures data reliability, so is it not redundant to use an MPEG Transport-Stream over TCP?
CDNs. CDNs make delivering small static HTTP objects much cheeper due caching efficiency, supply and demand, and stateless servers (hence more viewers per server). Second is live video. HTTP does not really work well given a file of infinite length. Hence breaking the stream into segments to make the CDNs job easier.