The
scaleable, sustainable solution for global OA is for each author's own mandated institutional repository to be the designated locus of deposit for all published articles. These can of course also be exported to any other locus desired (actually only the link need be exported, once metadata interoperability is ensured).
Arxiv depositors will of course be able to keep on depositing directly in Arxiv as long as they wish. Why not? They were, after all, among the first wave of OA providers, and have been faithfully doing it for decades, unmandated. Their Arxiv deposits can instead be harvested back to their institutions instead of trying to make these heroic depositors change their long-standing and progressive habits because other disciplines didn't have the sense to do it unmandated,
But it remains true that today most papers (across all disciplines) are not being deposited in Arxiv, nor in institutional repositories, nor deposited anywhere within the first year of publication. Mandates from institutions and funders will remedy that.
But for mandates to be effective, they must demand minimal effort from authors and institutions, and it must be possible to monitor and ensure compliance.
The simplest and surest way to monitor and ensure compliance is for both institutions and funders to require convergent deposit in the author's institutional repository. That covers all papers, funded and and unfunded (except the tiny minority by institutionally unaffiliated authors, who can deposit directly in institution-external repositories),
On the web, distributed locus of deposit does not "fragment the literature." No one deposits directly in google; google harvests. Google currently inverts all data and still has the best search functionality.
Once enough of the OA corpus is deposited in institutional repositories (IRs) to make it worthwhile bothering, it will be a piece of cake for an enterprising grad student to write the harvest and search code across the global network of OA IRs, and generations of grad students will continue optimizing these tools beyond even the imagination of today's sluggish, non-depositing scholarly and scientific researcher community...