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.
But is this idea, launched many years ago to complement "classical" 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?