PresuppositionsI find that I often read my academic colleagues' papers at academia.edu and other similar repositories, or they send me their drafts directly. I am not always aware of whether the paper has been published or not. Sometimes I can see that I'm looking at a word-processed document (double spacing, etc.); other times the paper is so smart it's impossible to distinguish from a formally-published piece of writing (LaTeX etc.).
Reading colleagues' drafts gives me access to the cutting edge of recent research. Reading in a journal can mean I'm looking at something the author had finished with one, two or even three years ago. In that sense, reading drafts is like attending a conference. You find out what's going on, even if the materials are rough at the edges. You participate in the current conversation.
In many ways, reading colleagues' writings informally like this is more similar to the medieval ways of knowledge-exchange that were dominated by letter-writing. The most famous example is Mersenne (fl. 1600), who was at the centre of a very important network of letter-writers, and just preceded the founding of the first academic journal, Henry Oldenberg's Philosophical Transactions of the Royal Society (founded 1665).
What am I missing?
Editorial controlWhat I don't get by reading private drafts is the curatorial intervention of a board of editors. A journal's editorial board acts as a gatekeeper for knowledge, making decisions about what is worth propagating and what is not worth propagating. The board also makes small improvements and changes to submissions, required since many academic authors are poor writers, and because of the natural processes of error. So, a good editorial board makes curatorial decisions about what to display, and improves quality.
Counter-argument: Many editorial boards don't do their work professionally. The extended "advisory board members" are window-dressing; the real editorial activity is often carried out by only one dynamic person, perhaps with secretarial support. This depends, of course, on the size of the journal and the academic field it serves. I'm thinking of sub-fields in the humanities.
Archiving and findabilityA journal also provides archival storage for the long term. This is critically important. An essential process in academic work is to "consult the archive." The archive has to actually be there in order to be accessed. A journal - in print or electronically - offers a stable way of finding scholars' work through metadata tagging (aka cataloguing), and through long-term physical or electronic storage. If I read a colleagues' draft, I may not be able to find it again in a year's time. Is it still at academia.edu? Where? Did I save a copy on my hard drive? Is my hard drive well-organized and backed up (in which case, is it a journal of sorts?)?
Counter-argument: Are electronic journals archival? Are they going to be findable in a decade's time? Some are, some aren't. The same goes for print, but print is - at the present time - more durable, and more likely to be findable in future years. An example is the All India Ayurvedic Directory, published in the years around the 1940s. A very valuable document of social and medical history. It's unavailable through normal channels. Only a couple of issues have been microfilmed or are in libraries. Most of the journal is probably available in Kottayam or Trissur in Kerala, but it would take a journey to find it and a lot of local diplomatic effort to be given permission to see it. Nevertheless, it probably exists, just.
PrestigeA journal may develop a reputation that facilitates trust in the articles published by that journal. This is primarily of importance for people who don't have time to read for themselves and to engage in the primary scholarly activity of thinking and making judgements based on arguments and evidence. A journal's prestige may also play a part in embedding it in networks of scholarly trust and shared but not known knowledge, in the sense developed by Michael Polanyi (Personal Knowledge, The Tacit Dimension and other writings).
ConclusionAt the moment, I can't think of any other justifications for the existence of journals. But if editorial functions and long-term storage work properly, they are major factors that are worth having.