HTTP keepalives prevent the excessive connection requests. The main issue with HLS distribution is TCP sucks over high latency links, so you have to have edges near your users.
Gotcha! I've also heard of people using WebRTC to reduce latency by setting up a direct-to-user link between the ingest server and the end-user? Any idea how this helps?
Beam (recently acquired by Microsoft) does very similar to this. Rather than wait for the whole X second segment to be built and distributed, they apparently stream MPEG atoms through websockets which are them reassembled in JS and presented via media source extensions. At this point you may as well have re-invented RTMP, minus the Flash dependency :).
In addition there is a major encoding downside to this. If your encoder can grab a whole 2-10s chunk of video it can produce a better quality stream. This is actually _super_ important for producing good video quality (especially on things like sports streams).