An average paper from arXiv has 10 people in the world who can appreciate every detail of the text, half of them are the authors, their advisors, and paper's referee, the other half will be mentioned in the acknowledgements. This is especially true e.g. for mathematics. I want to point this out because papertalk.xyz features many texts like that.
Moderating some kind of "official" internet forum for papers will require a lot of time, and most researchers won't bother to follow it, because messages will be of low value, from crackpots and occasional ill-spirited anonymous commenters.
In 2016 arXiv run a survey about new features. Comment section, votes on submissions etc. were not popular. Many people were against this stuff, so it was not implemented.
There have been projects like PubPeer that tried to explore this territory and never really took off.
I see a value in a website like HN with links to papers of bigger interest and discussions for the general public.
E.g. someone posts a link to a new publication/preprint about cancer research, a supposed superconductor discovery, massive high energy physics experiments, etc. and users are free to discuss the meaning, beauty, impact, and credibility of the results.
But I'm not sure if this can work for mundane papers that are >99% of published research. I also think it will be much harder to market to the researchers. As someone who read, wrote, reviewed papers.