Thanks for the pointer; I'll check out that model and see if it handles the "slowly and carefully" type of recording better than the "natural speaking" type. (And depending on what kinds of errors the model makes, even the recordings where it makes errors can prove useful: for example, a linguist studying regional variations in speech would want the model to produce the IPA for "gonna" rather than "going to").
Example: Schwabisch is wild and would be phonetically transcribed very differently from Hochdeutsch which is its ostensible language progenitor (technically more a cousin than an ancestor in the lineage of language evolution), but if the goal is merely to focus the model purely on phonetic transcription then you can add additional post-processing layers which map sounds to core concepts shared across dialects for actual translation. But I like your idea of interacting with the intermediate elements to familiarize yourself at least with the phonetic patterns, we humans are still thinkers enough to infer patterns of grammar and semantics from these building blocks just as we have done for the entire history of the species/lineage before written representations of language came along (relatively late -- evidence of script cropped up only once civilization had centralized to a sufficient degree to make economics non-local and non-trivial).
tl;dr the big words: it's not til you collect enough spoken samples of the dead(ish/dying) language being spoken that the local idiosyncracies are discovered, luckily linguists are smart enough to probably anticipate and certainly post-process language snippets to grasp the common structures for this or that given language.
That's true if you mean "very rarely spoken" literally, as in even the native speakers don't get to use it very often. But many languages aren't widely spoken (such as only in a certain geographical area, which sometimes is only a single village, or other times a small number of villages). But inside that area, they are frequently spoken. And you might be surprised how many of those small-geographic-area languages still have distinct dialects.
For example: my wife (a linguist) did her master's thesis on the pronunciation of a language with about 7,000 speakers, and identified how many distinct dialects there were. (Which is why I know a little bit about this). She recorded native speakers from all 13 (I think it was 13, but it might have been 14) villages where the language was spoken, and found five different dialects, which she grouped into two "main" dialects. (Think American vs British in the English language, with subdivisions into Midwest, New York, and New England accents and so on, and you'll have the right general idea — though these dialects were closer to each other in sound than Midwest vs New York). I'd have to go reread her thesis to give you any more details. But this was a language that was only spoken in a small geographic area, but it was frequently spoken, because that was the main language of those villages. (The country's official national language is what the kids learned in school, but some of the people, mostly those 60 years old or older, hadn't gone to school, because the first government school in their area was only built 60 years ago -- so they only spoke their minority language, and not the country's language, and their kids had to translate for them if they had to leave their village and go shopping in a major town).