Why do we not reinvent the journal system?
Please meet the Open Access movement. In the last twenty years, many scholars and librarians did try to address the problem you pose. It is, in fact, a huge issue, and things like this don't change overnight.
The OA movement focused on two main strategies:
Publishing in peer reviewed open journals (gold open access): the idea is to create a brand new journal (or to change the model of an old one) which will provide articles free for the readers, without the current subscription model in which libraries (meaning, taxpayers) pay. The crucial factor of Gold OA is the presence of peer review: organize real journals costs a lot of money, and at the moment the major business model is APG (author processing charges), meaning that the author (often, the faculty behind it) pays for being published and cover the journal costs. We're still in transition, and there are a lot of drawbacks: there are predatory publishers who try to scam authors, and big publishers offer the "open access option" charging huge fees (this is also called double dipping, because a hybrid (both Open and Closed) journal will receive the money from subscriptions and the money from the authors. It is important to remark, also, that big publishers make a lot of money with subscriptions and they are actively challenging the open access model. PLoS, for example, is one of the new Gold OA publishers.
Self-archiving in repositories (green open access): it is the model of arXiv, Repec, and thousands of other repositories. They can be "institutional" or "disciplinary", and they accept mostly pre-prints, but also post-print articles.
Of course, there are some experiments in the field:
- PeerJ has a very interesting business and pricing model.
- Epijournals (from my understanding) are journals created selecting papers from arXiv and other repositories.
References
- Open Access, by Peter Suber, MIT Press, 2012.
- Wikipedia "Open Access" article. Accessed 4 Jan 2015.
Full disclosure: I've worked as a digital librarian in managing OA journals from University of Bologna. I'm biased towards OA and open knowledge in general. Please keep it mind that my answers reflect these bias.
The traditional publishing model has in fact been heavily debated over the past decade or so, and there have been several reinventions. Among these are Open-Access journals, repositories like arXiv, academic social networks like ResearchGate and publishing the paper and the data through repositories such as GitHub.
Some of these are also attaining a great deal of success. The biggest reason we're "not there yet" is inertia. There are two reasons for this inertia.
- Publishers don't want to lose their revenue stream, and produce propaganda claiming open access or other alternative models don't work, and traditional paywalled journals are the best.
- There is a very strong culture of judging the worth of research by the journal it's published in. So in practice, if you have a very good paper, you make a decision: Do you compromise on your pro-OA sentiment and publish in a prestigious journal, or do you risk undermining your future job applications by publishing in an OA journal?
Ultimately, it appears to be the case that applicants who are seriously considered will be evaluated on the merits of the papers themselves, not where they published. However, when there are hundreds of applicants for a position that need to be quickly screened, will the overworked committee have time to read several papers of every single one, or will they start scanning the CVs for journal names?
OA will surely prevail in the end. Recent past has shown that in practice and in theory, there are no major reasons why it shouldn't. Perhaps after that, other more revolutionary changes will follow. However, OA will not "win" until faculties overcome the bias that OA journals are lesser journals and papers published in OA journals are not good enough for traditional ones. When they do overcome this bias, post-docs and graduate students will happily switch to publishing in OA, now that it's not endangering their career.