There are still problems:
1.) Usually old papers are not available via this route. If you email the author and ask nicely he will usually send it to, but at least in pure mathematics one quite common wants to look up really old articles, say from the 1950s, and those are the ones that are terribly hard to come by, because they are often only available behind a paywall like JSTOR.
2.) Currently "prestige" and peer review is handled through the journal system: Authors send their papers to a journal for publication, other scientists review them (for free), and then the paper gets published (or not). Afterwards publishing houses, who add little value to the process, force libraries to pay horrendous amounts of money to get access to these journals (usually through selling bundles).
At the moment there are efforts underway to pleasure publishers into a saner pricing structure, and there are now some open access journals where usually the author pays once (if at all) and then it is free to read for everyone.
Many people also consider more radical approaches, for example, making journals simply be ArXiv overlays that point to a set of papers on the ArXiv. I have even heard suggestion of replacing peer review, at least partially, by an open review system like you suggest, and some journals have experimented with it, but it does not seem to have a lot of consensus behind it at the moment. But this is in a way orthogonal to the problem of making research available to as many people as possible.
The problem with the very radical change that you suggest, i.e., using blogs instead of research papers, is that peer reviewed papers have proven their worth over a long period of time. It is doubtful whether simple blog posts would guarantee a similar quality over a long period of time. My personal feeling is that there would be a lot of noise and incorrect stuff drowning out the important stuff.
With regards to your edit: If you submit a paper that seems to be serious research to a journal, it will be reviewed, and if it holds up, eventually published. If the paper is decent, you'll be able get it published without being associated to an academic institution (at least in mathematics, can't speak for other fields).
It seems like the real issue here is prestige, which then translates to funding. "Publish or die" is how most researchers seem to live. Thus I think if we are able to show that self-publishing/distributed publishing brings the money to the researcher and the academic institution then this idea would get traction.
Re: edit. I see. That's great to know.
I think that Terrence Tao https://terrytao.wordpress.com/) has an interesting take on using blogs for math: He publishes in journals, but uses his blog to post lecture notes as well as short summaries of some of his papers.
But then this is not so different from a typical academics homepage: Usually you will find a list of publications (hopefully with PDFs, at least for the newer ones) and lecture notes there. But of course it differs for each author, and perhaps other fields have different conventions.
> But of course it differs for each author, and perhaps other fields have different conventions.
I think this is also spot on. The research lab where I worked was a collaboration between the Physics and Chemistry departments. The technology used by the two chief researchers was radically different, despite having worked together for decades. For example, my professor and his sub-group (Physics) used LaTex to typeset all his papers. The Chemistry professor and his sub-group, OTOH used Microsoft Word. From what I understood that was pretty common for the respective fields. So much opportunity here as well as so much resistance in just these types of issues...
> It seems like the real issue here is prestige, which then
> translates to funding. "Publish or die" is how most
> researchers seem to live. Thus I think if we are able to
> show that self-publishing/distributed publishing brings
> the money to the researcher and the academic institution
> then this idea would get traction.
Perhaps a bit more of the stick and less of the carrot is what's needed... if they find carrots pleasurable, that is.