The big picture is that from the 1970s to 2013, a small group of commercial publishers had succeeded in gaining control of most academic publishing.
However, amongst the interesting points made is that the behaviour of publishing in the Humanities is significantly different from the situation in the Social Sciences and STEM. This paragraph from p. 7:
On the other hand, papers in arts and humanities are still largely dispersed amongst many
smaller publishers, with the top five commercial publishers only accounting for 20% of human-
ities papers and 10% of arts papers in 2013, despite a small increase since the second half of the
1990s. The relatively low cost of journals in those disciplines—a consequence of their lower
publication density—might explain the lower share of the major commercial publishers. Also,
the transition from print to electronic—a strong argument for journals to convert to commer-
cial publishers—has happened at a much slower pace in those disciplines as the use for recent
scientific information is less pressing [28]. Moreover, these disciplines make a much more im-
portant use of books [9] and generally rely on local journals [29], all of which are factors that
make it much less interesting for big publishers to buy journals or found new ones in the arts
and humanities.
(I disagree with the assertion that the transition from print to electronic is "a strong argument for journals to convert to commercial publishers." The opposite seems true to me, especially today. Perhaps this is a change since 2013, with the growing maturity and popularity of
OJS and the work of the DOAJ.) It looks as if our own fields have escaped the worst of the recent changes.
What all this means is that although OA is growing, there's still a long way to go and the publishers' Oligopoly is still very powerful. This can change if members of learned societies express their wishes to the leaders of these societies and their journals, and if founders of new journals take OA seriously as an important goal for the distribution of learning and discovery across all academic communities worldwide. Another vital component of change is for governments and major funding bodies to insist that the results of the research they pay for is published OA. That's Plan S.
Finally, it's also worth noting the effect of Article Processing Fees. Often, OA as implemented by the publishers' Oligopoly is coupled with the requirement for APFs. Without OA, colleagues in India cannot not afford to buy and read many books and journals. But in the old pre-OA model, they could publish, because article-acceptance was on merit, with no fees. When APFs are introduced into the business model, colleagues in the developing world can read OA publications freely, but they can often not afford to publish. It's a choice of being blind, or mute. The equitable situation is to have OA without APFs, i.e., for journals to find their funding from sources other than their authors.
Best wishes,
Dominik