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
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