I heard from Paul Ginsparg that bioArxiv's original raison d'etre was to give biologists more assistance in producing professionally typeset documents since far fewer of them know LaTeX then physicists. This was going to be funded by a submission fee of ~$50. That idea was apparently nixed, so that the difference with the arXiv are now mostly cosmetic (with the notable exception that bioArxiv has commentary).
Fractionalization is generally undesirable, but it's plausible that bioArxiv can make tweaks that accelerate adoption among biologists compared to arXiv.
Discoverability is a big part of it as well, at least at the user end. I find out about new papers from email alerts of subject matter and tables of contents of the new issue of the journals I keep up with. (Obviously when I need to look into a particular issue I use google scholar).
I have never once found a paper of particular relevance to my research (geology/geophysics) on arXiv. I haven't looked very many times, but after striking out several times, why keep trying?
If there was a geoRxiv then I would probably browse it more regularly because the chances of me finding something relevant would be much higher.
For that reason, and another, I kind of disagree that fragmentation (or fractionalization) is undesirable. The second reason, which is not unrelated, is that–at least with peer-reviewed journals–the quality of the work in field- or subfield-specific venues is often far higher than in the sort of pan-scientific journals like Science or Nature. I think a lot of it has to do with the quality of the reviewing/editing, but a lot of it is that the papers have to be written for and justified to a wider audience that wants to be wowed and doesn't know the background well enough to evaluate the science for its own sake.
If I write a paper and send it to Tectonophysics, I know that the readership will understand what I'm doing and why, and I will write the paper accordingly. If I write the paper for Nature, then I have describe and justify the how and why to a wide range of people from my peers to journalists for phys.org and the NYT. Sometimes that's fine: If I find out that the Seattle fault is loaded and ready to pop, the press, policy makers and citizens need to know. But if I find out that the stress field on the Seattle fault is largely determined by the topography near the fault and that has some persistent influence on how an earthquake rupture propagates on the fault (but doesn't necessarily change the seismic hazard) then I don't need to go through the rigmarole of explaining and justifying any of that to anyone who isn't intrinsically interested, and maybe more importantly, I don't have to explain (i.e. gloss over) the subtleties, ambiguities and caveats of the work to an audience that lacks the relevant background. This simply allows me to write a more clear and more honest paper.
This brings up a tangent that is relevant to the broader topic of self-publication: You always need to write to a specific audience, and with a journal you know who that audience is. With a blog or a website, you don't necessarily. That may be fine but it can trip a lot of people up, and make the writing much worse.
The arXiv serves to unbundle the dissemination part of journal publishing for the filtering and certifying part. The arXiv is only trying to disseminate, and it is happy (for now) to let traditional journals and other sources do the filtering and certifying.
Let me reply to your points in particular:
> Discoverability is a big part of it as well, at least at the user end...If there was a geoRxiv then I would probably browse it more regularly because the chances of me finding something relevant would be much higher.
Are you just talking about the individual subject areas (ecology, genetics, etc.)? The arXiv has those as well, which you can subscribe to. Few physicists subscribe to the entire thing. (Incidentally, folks may find https://scirate.com/ filters a bit better.)
Of course, the arXiv doesn't have a dedicated biology section, much less sub-divisions, but this is because there hasn't been enough interest.
> The second reason, which is not unrelated, is that–at least with peer-reviewed journals–the quality of the work in field- or subfield-specific venues is often far higher than in the sort of pan-scientific journals like Science or Nature.
The main point of the arxiv is to put everything in one place which is permanent, searchable, sortable, freely available etc. Filters generally come from elsewhere, such as the aforementioned sections or SciRate, or by simply looking at arXiv papers published in certain journals (without needing journal access).
Obviously, in the absence of additional filters, the bioArxiv won't be useful as filter either.
> If I write a paper and send it to Tectonophysics,...
You'll find that there are plenty of popular-level papers on the arXiv sharing space with highly technical ones. This is generally noted in the abstract. While the arXiv is not meant for public consumption, there are plenty of filters that try to pluck out accessible papers, e.g., the Physics ArXiv blog (which isn't as official as it sounds) https://medium.com/the-physics-arxiv-blog
> to give biologists more assistance in producing professionally typeset documents
So why does it seem like Greider's paper received none of that assistance? It's typeset in double-spaced Arial. Both double-spacing and Arial are immediate indications of unprofessional typesetting.
Fractionalization is generally undesirable, but it's plausible that bioArxiv can make tweaks that accelerate adoption among biologists compared to arXiv.