I don't know. I think the act of forming a paper up from scratch is an essential element in the process of research. It really isn't a waste of time and space in the sense that proper research will require these definitions and preliminary results be carefully reviewed by the author anyways. Why not have them type it out for us? Or for their own sake even.
A wiki style database of information could be an exciting resource for kicking off new ideas. When scientists conduct research within this database though, findings and methodology must be to a high enough standard. Marks of high quality research include well defined terms and contextualized prior results.
If you want to get straight to the new information, read the abstract up top, skim the middle and read the results and discussion.
I completely agree that serious researchers should review definitions and results they are basing their findings upon. But then, I'd find much more reliable an editable reference paper corrected and improved by a significant number of people working in the field, rather than an old-style paper, published decades ago, after a (botched ?) review by a couple of anonymous reviewers, and not revised since then.
This would address also a little bit the problem of notations: if everybody agree and work on the same piece of work, they are likely to adopt the same notations, providing a nice coherence to the user.
A wiki style database has many advantages when it comes to organizing and searching information. In my opinion, though, the editing process should be closer to GitHub's pull request (as advocated by the article), to ensure that everything is properly reviewed before publication.
Finally, a publication scheme like the one I described also address a recurrent issue with traditional citation-based papers: citations are one-sided. It is easy to see which papers one article depends upon, but the converse is hard (unless using specific tools, at least). With collaborative editing and wikipedia-style links between articles, the reader is immediately aware of the latest findings in the field, which simplifies tremendously the bibliographic research.
A wiki style database of information could be an exciting resource for kicking off new ideas. When scientists conduct research within this database though, findings and methodology must be to a high enough standard. Marks of high quality research include well defined terms and contextualized prior results.
If you want to get straight to the new information, read the abstract up top, skim the middle and read the results and discussion.