"Do you think there's room for a new discussion site which embraced all these lessons that other discussion sites seem to perpetually be ignoring (perhaps due to simple entrenchment)?"

There's a ton of discussion sites. It's not "reddit or HN or nothing"; it's a question of which of the bajillion forums, blogs, link aggregators, email lists, or other things you're interested in joining. There's room for all kinds of more of them, too. There's so many choices it's more a discovery problem than an availability problem.

However, if you go into it with the hopes of being the next thing that is the size of Reddit, statistically, you're going to be disappointed.

It isn't even clear to me that this is a very good goal, either. Running a site the size of Reddit is an enormous, enormous hassle. The controversies currently associated with it at the moment are merely specific instantiations of the general fact that you can count on being vilified by a good 20%+ of the community once you reach that size, that every change will be met with a huge outpouring of hatred straight into your contact box, and so on. Goodness help the poor person trying to start The Next Reddit (TM) with the naive idea that it is a good idea to be very available to the community... all that does is add to the inevitable flames some fresh flames when you have to reneg on that promise too. Unless you've got a solid plan to monetize enough to make it worthwhile, fast enough for it to be worthwhile, while still somehow organically growing without that getting in the way, I'd suggest shooting for starting a community for $X, for some value of $X of interest to you, rather than trying to be The Next Reddit (TM).

fantastic points, and spot-on about aiming for a solid community (if small) over "the next Reddit"

What lessons would you like to include on such a site? Off the top of my head, my favorite things about Hacker News: high level civil discourse, lack of humor (no, seriously, humor easily crowds out good discussion on other sites), excellent layout (collapsible tree comments), anonymous speech with ease to creating new accounts, light handed and responsive moderation. There's not much I don't like: narrow focus on tech rather than just general good content (but that is why it was created), no easy way to collapse a comment tree when you've scrolled partway through it, and... that's really it.

What specifically would you like to differently? I'm interested in more good discussion sites.

I could say "upvote category" (a la Slashdot or Steam where you can tag a comment as "funny" or "insightful") and "downvote category" (so you can specifically downvote for disagreeing vs. offensive vs. irrelevancy) but let me tell you a story about Reddit instead.

Once upon a time I was subbed to /r/redpill, usually to counterpoint their many arguably-false conclusions. Naturally I was downvoted to oblivion most of the time, because Reddit does not do anything to prevent echo-chambers (in fact it probably outright encourages them... because engagement), and thus, echo-chambers are a natural result of subreddits and "comment percolation via upvoting in agreement and downvoting in disagreement" (the fact that Reddit TOS says you should only downvote on irrelevancy, NOT disagreement, doesn't matter, because people are assholes and critical-thinking skill is apparently an extremely precious commodity these days).

At the same time I was subbed to a number of, eh, feminist subs, like TwoXChromosomes. Sometimes, I disagreed with them too (and got downvoted), but most of the time (slightly most of the time), I got upvoted on those.

One day, I got banned from ALL feminist subs. ALL. OF. THEM. Simply because some mod with a god complex did a cross-reference of everyone subbed to /r/redpill, and mass-banned them. My entreaties to the mods ("just look at my fucking comments in there! I'm actually fighting for you guys!!) resulted in no reinstatement. (While this should not matter, it probably didn't help that my username at the time was "GSpotAssassin".)

Around that point, I kind of lost faith in Reddit as a thing not fatally-flawed. (While deciding to completely step out of the modern gender wars. It's a cesspool, anyway.)

I cannot emphasize how much I loathe echo-chambers. And it seems to be getting worse. I literally do not understand how people cannot tolerate the occasional discomfort of a dissimilar viewpoint, especially if it is well-argued. But I'm a rationalist, and we love a good debate, basically. Sadly, this does not at all account for most people, who I like to joke "prefer to belong than be right".

I guess the problems come with the fame. As long as you are a small site, you can do pretty much whatever you want, but as you grow, you have to compromise in some way. You can bend to advertisers and lose some of freedom, or go down the chan way and get a name that reflects what you have to offer and probably have a revenue that is consistent with that.

On top of that , there's the fact that the average user, simply doesn't care about all this freedoms or number of upvotes and stuff like that. They just want content and reddit right now has enough for everyone.