As far as I remember, huge portion of the "old web" web was self-curated list of human-to-human channels: be it blogs, BBs, rss, news/usenet, heck even irc, or whatever personal oddities. I will never forgive Google for killing Reader to promote g+.
The facebooks of today make it effectively impossible to self-curate attention. Social media is the publishers early internauts tried to get away from.
I disagree with your last paragraph, though. The "old web" was a small walled garden. The "post slop" web is going to be very similar small walled garden, that is chased to get away from uninspiring everyday.
Here's a free idea for anyone hoping to launch anything like this: implement a MLM style transitive web of trust. The forum is invite-only. x strikes - you are out, but the strikes on invitees transitively decay over the invitation chain. If you invite someone who then invites all the normies who get striked out - eventually that strikes you out too. Invite yourself to shitpost - eventually you will get punished for that. Yes, it's bad as it can exacerbate bubbles as much as the current facebooks do. Simple updoot mechanism suffers from brigading, but something can be worked out.
I agree the web-of-trust model is a good idea for the future. Lobsters has something sort of like it in that you can see a tree of who invited who. I don't think it has a fully fleshed-out system for reputation flow on that basis though.
I don't think the old web was really a walled garden, though. It was just a sort of isolated garden that was harder to get to. There was nothing outside it threatening it. Now the garden needs walls because there are a lot of dangerous things outside.
No dooting. Let it be simple chronological, or unread first. Dooting creates an echo chamber because the most dooted thing is the most viewed thing so it gets more doots.
Dooting does not have to be contribution ranking mechanism, it can be contributor ranking mechanism, which is a bit less likely to succumb to bubbling. Otherwise, yes, dooting is one of the core pillars of facebookization.