I would like to share the particle physics example on this topic (that is a very important one). I think my field has one of the best practice on that matter.
First, all particle physics preprints are on the arxiv. This is a general rule in the field, and this holds for at least 1.5 decade (it was already the case when I started my PhD years ago). The papers are then submitted to journals from the arxiv directly (the arxiv number is sometimes even mandatory for the submission to proceed). This guarantees that all texts are available for free, by anyone.
In addition, all our most important journals are open access thanks to the SCOAP3 initiative. To make it short, CERN in particular an other big institutions pay the journals a fee to make all particle physics article free and open. That's not ideal, but this is at least good for making science freely available to the general audience.
And finally, we have the scipost initiative, an online journal by physicists and for physicists, completely open, transparent and free. It is somehow the arxiv equiped with a publicly available referral system. Referee reports and associated replies are all public (which also changes things in the better way) .
I have personally not published that many papers in there yet, as some universities / institutions do not recognise scipost as a real journal (and this is problematic when younger ones are involved in a paper). However, things are slowly changing. I am hence now writing two papers, with young collaborators, that should end to be submitted to scipost within a month or two.
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