You're fortunate to even get to. this stage. In my experience, on both large and small subs, even this very rarely happens.
Part of this is the fault of threaded presentation -- very useful for following a specific subthread, but horrible for seeing where a discussion remains live. HN suffers from this as well. Unless you can alternate flexibly between various threaded vs. flat time-ordered presentations, or even randomly-selected contributions, you're not going to break out of this.
A real challenge is that as conversation, functional scale is low. At least one person, more usually at least 2. I've noticed that panels with more than three participants (live, radio, TV), and usually as host/moderator + two guests, do poorly, often due to the timeslicing problem -- an "airtime hour" is effectively ony 50 minutes, with a Q&A and after introductions, speaking time is often only 20-40 minutes. Divide that among participants, and by the time you're at 4-8 minutes per participant with 5 panelists, fewer still with more. Usually the form devolves to a loosely coupled set of short serial speeches or lectures rather than actual engagement.
With more time -- hours at a symposium, Socratic lectures, a long dinner discussion, an academic seminar -- it might be possible to bump the size up slightly -- there's more time to discuss, or (academic) more focus. But even here the ideal size is 5-15 participants (see for example: https://sites.google.com/site/entelequiafilosofiapratica/aco...).
Text gives the potential for expanding this ... slightly. Maybe about 50 people, possibly double that with an excellent moderator. Yonatan Zunger at Google+ is among the best I've personally witnessed. Sadly the archived conversations at the Internet Archive preserve only a small number of comments.
Group size, intragroup relations (do participants know and respect one another, even where they disagree?), avoiding perils of groupthink (self-selection, unconscious group bias, self-censorship, privilege, cultual mythologies, etc.), and a fair-but-firm moderation, are all critical. And you're still lucky to apprach, let alone exceed, Dunbar's number (about 150).
Last I checked, there were slightly more than 150 people online. This means that there'd have to be on the order of 10^7 individual conversations, minimum, more likely 10^8. FOMO much? Group concesus and information sharing are ... profoundly limited.
HN has, as I understand, has on the order of 10,000 registered users. (A very rough guesstimate.) As of 2013, daily uniques was about 200,000 (see, with interesting discussion of some site-design parameters: https://techcrunch.com/2013/05/18/the-evolution-of-hacker-ne...). Looking over the list of just the top 100 users (https://news.ycombinator.com/leaders), I recognise many, a few personally, and shave one, but ... really can't say I've got a relationship with the vast majority. And that's ~0.01% of registered users, 0.0005% of daily visitors.
And just to note: I'm agreeing with your comments. I just see them as the tip of the iceberg and part of a problem that goes far deeper than mere technical aspects.