There's no personas, developers don't have three different brains they keep in the fridge and swap the ones in their head with.
Just admit that sure, interweaving information to get good quality docs is exhausting. And that we invented this "write for an audience" crap to simplify the work of the writers - "we're lazy or we have limited resources for writing docs, that's why we're doying it this way".
It's the same for writers and journalist, the "write for a specific audience" trick is way to lower the effort needed to get reviews / publishers' attention / clicks / views / shares etc. You do it when you're getting started if you ever want to get started I guess. But large scale it produces shallow literature, hard to fact check or contextualize journalism etc.
You do it for yourself (the writer) or to save resources for your companies (sure, interwoven/mixed docs are hard to maintain - I'm not even sure how eg. Pytorch's team manages to do that, but probably being the leading ML frameworks attracts top talent from the whole planet to one open-source project so it's doable for them...). But don't sell the bs that you're doing the reader/consumer any service, keept it hones to yourself and others!
> a single disorganized pile
Nobody proposes a "single disorganized pile". Sure, it's hard to eg. put bite-sized examples + condesed 'why' explanations into API docs and to maintain such docs, but it's doable - in the ML community some people use notebooks for docs wiriting and sometimes even for development by generating the code from them (sure, this is utterly extremist and I don't like it myself, but it works for some), some kind of renaissance of "literate programming".
I don't say we revive literate programming, but going haf-way between that and "a disorganized pile" is what I meant.
That said, I'll agree that these should be interlinked. A tutorial that doesn't ever link to practical how to's is terrible, and please include references to theory in your api docs so I can gain a deeper understanding when the design doesn't make sense to me, etc etc. It's easier to write and read when you are assuming the audience of a particular work; you can switch roles when you click on a how-to article, but trying to inhabit all personas at once is exhausting and unproductive.