[1] http://blog.jessriedel.com/2015/04/16/beyond-papers-gitwikxi...
[4] http://blog.jessriedel.com/2015/05/20/gitwikxiv-follow-up-a-...
[8] https://medium.com/@samim/gitxiv-collaborative-open-computer...
I agree with @xvilka that there is lots of room for innovation and exploration, but even in the more traditional setting there is some movement coming from the smaller realities. It seems to me that the big publisher monopoly, which at least in my field is completely unjustified, is the bigger obstacle.
[1] https://discreteanalysisjournal.com/ [2] https://www.emis.de/journals/SIGMA/ [3] https://jep.math.cnrs.fr/index.php/JEP/ [4] https://www.elibm.org/series?q=se:2204 [5] https://intlpress.com/index.php [6] https://aif.centre-mersenne.org/
Essentially it's 'Reddit + Patreon for research'.
The large number of submissions is indeed a problem for other fields (I think mostly computer science?). I'm not sure what the best solution is for that. A voting system (where you see a mix of new and popular submissions), together with some content filtering, can help the reader. However, this would probably lead to some important papers getting burried.
There's still very much a distinction between (self-)publishing on the arXiv and publishing in a 'real' journal/conference within the academic community, and I think it comes down to two factors:
1. The arXiv moderation process has a much lower bar; you see some pretty rubbish papers (often from large tech companies) make their way onto the arXiv which would never be published in a 'real' journal; ultimately this isn't a shortcoming (the arXiv has had a monumental impact on academia), but rather that the arXiv isn't trying to be a peer-reviewed journal.
2. Visibility/'impact' is lower on the arXiv; there are ~14k submissions per month, so inevitably the signal to noise ratio is low.
I feel what we really need is for a few universities to put the many millions they spend on annual subscriptions into some kind of endowment to pay for proper editorial boards for a peer-reviewed arXiv instead, open access, perhaps with a token fee for submission (or a slightly higher academic affiliation bar). I think if two or three big universities from each of the US/UK/Europe suddenly made this change we would see the death of academic publishing in months.