(Why) Is post publication peer review (not) taking off? I know, this is a bit of a broad question. But looking at the developments and having experienced a reasonable amount of pain with established publishers and their either complex, slow, or restrictive processes/production stages, I'm tempted to ask it here and look what others think or know about that.
Post-publication peer review has been discussed quite a while ago here and here, it's been promoted and practised on platforms such as Publons and PubPeer.
But is this idea, launched many years ago to complement &quot;classical&quot; peer review, really successful? Are established processes/practises being replaced/improved?
Note for clarification:
I envisage something like a combination of classical pre- and an optional post-publication peer review strongly based on open self-archival platforms such as arXiv. Nothing on the academic side would change, editors and reviewers would move over to such platforms to continue their work just like before, largely unpaid. Even cult-like reputation-building, gate-keeping, etc. is still possible even if not desirable. But in domains such as CS, physics, or math, where production is largely done by authors anyway, costly, error-prone, after-acceptance production stages would be replaced by just self-archival and EiC-driven quality labelling systems as they have been used for years at top-tier conferences to certify such things as reproducibility. I think, it's time for a change. (I wonder whether this question is more something for meta.)
Further note: After the many useful comments and answers, I'm extending or rephrasing my question to: Why isn't full-fledged self-archival with classical peer review and curation, post-publication commenting, and avoidance of old-school production procedures finally taking off?
Most papers that are published are uninteresting.
The median paper has less than one reader not counting the authors and the reviewers.
The current reviewing system relies on a network of responsibilities that are independent of the author.  The editors have a responsibility to the community as a whole to get papers reviewed properly, and the community gives them esteem for performing this duty.  The reviewers have a responsibility to the editor to actually do reviews, and the editor is usually some influential person (and in any case will probably at some point be the editor for one of the reviewer's papers).
Suppose I have written one of my usual mediocre papers that is among the 70% (my estimate) of papers that are never read.  How would post-publication peer review be organized for it?  If I have to find reviewers myself, then everyone is going to say 'No' or do a bad job, because no one feels any need to impress me and it's not a very interesting paper to read.  Moreover, the best reviewers for my paper are people with a little higher status than me, and they would definitely say 'No' to me, but they might say 'Yes' to an editor.  (Keep in mind that, as the system is set up, some top people in a field do far more reviewing than they write papers, while many people write one write-only paper every several years (or grad students who stop doing research write one paper from their dissertation) and never review.)