Sure I've heard about Impact Factor ratings that all public universities heed to... but I've also heard that you do peer-review for free, and publishers earn money from letting people read papers, and letting people publish papers as well. Wouldn't it make more sense to simply publish PDFs on own websites? Or just sell them in own webshops?
It would be much harder to find things of interest to almost everyone. Subscribing to a journal (or having the library do so) is a form of concentration of ideas that makes them easy to find.
And the review process helps people know what is valuable without having to do their own analysis of every paper. Many can rely on abstracts and summaries without having to verify every fact and re-test every hypothesis.
I've successfully self-published books, but the only reason they were successful was that everyone who had any interest in them already knew how to find me and my website. But for those books that didn't have a pre-existing audience? Nada.
Search engines can only do so much.
Note that the world was once like that, say in the 1600's. It was very hard to disseminate new/good ideas and just as easy/hard to publish junk. Progress has been made, though the world isn't perfect.
You can, of course, publish on your own. No one stops you. But you will find only a tiny audience in almost all cases.
I myself do think that people should put their work on their web pages, available to The Universe (=internet?)
I do put online everything I write, and in the last 20+ years have kept a mind about copyright issues with publishers, so that everything is legit.
It is true that, if one is not well-established in one's field, such self-publication scores no status/establishment points... while it still can obviously benefit everyone.
At a certain point, if one is not straining toward tenure or higher-status in some way or other, but has established oneself as a fairly reliable scholar, I think self-publication is the socially perfect thing. (Oh, yeah, nevermind pay-raises...)
Again, yes, if you have tenure, and are not concerned with payraises related to conformity... indeed, publish (!) on your academic web-site. :)
It is not true that no academics self publish, although it is not very popular indeed.
Firstly, the fact that a book is self-published, does not mean that it hasn't been peer reviewed, or that it must be of low quality. I have bought and read two self-published books (this and this) and I found both to be of excellent quality and rather insightful.
Moreover, several people make their lecture notes available on their university websites; this is a form of self publication. Such material can often be better than many published textbooks.
Robert Ghrist has published a book titled "Elementary Applied Topology" on Amazon. I haven't read it, so I don't have an opinion about it. It is interesting to read his blog post "why I self-publish my mathematics texts with Amazon". The reasons he mentions are: (i) he retains all copyright, (ii) he can set the price, (iii) custom style (figures, etc), (iv) good distribution around the world, (v) good quality of production, and a few more.
In the same post, he addresses some of the concerns people often have regarding self publication.
When it comes to papers, arXiv and other similar repositories have become very popular. Many publishers allow the authors to make a preprint of their paper available on arXiv or on university repositories.
Regarding your question about why the academic don't sell their papers via alternative channels, I believe that the majority of academics are simply not interested in selling their papers.
If you consider putting PDFs on websites to be self-publishing, then I, and many other academic scientists, self publish. Most of the papers are posted on our websites and also published in journals.
In much of academia, a publication does not count towards career advancement unless it is peer reviewed. The reason to use a traditional publisher is to obtain the peer review, not to disseminate the publication.
ArXiv is a better way to spread work than self-publishing or traditional publishing.
I know a professor that ONLY self-published for a while, because after his Ph.D. he wasn't accepted into any post docs or teaching positions, so he wrote 6 books on the same topic, got relatively well-known, and essentially became an authority on it; after which he got the professorship. His path is quite unorthodox, so they do self-publish, it's just rarer.