As an Africanist, I can tell you that the types of critical analysis applied to oral history differ because the disciplines involved--and the amount of potential corroborating evidence / contrary evidence we know about--are very different than in the Classics. For example, the critical views of a lot of the Western canon come from archaeology and newer sources' analysis that isn't as thick on the ground (or had time to dig/density of discourse to develop in the same manner) for non-Western sources that are often far less numerous. Basically, for a lot of the material I work on, we have either oral history, linguistics, anthropology/archaeology (linked in the US), and rarely a bit of several; in the Classical mediterranean, however, there's arguably been a lot more work done and a lot more written.

Personally, I'd love to see the recovery of narratives and physical evidence of such strength that it could throw the story of (say) Sunjata Keita into doubt; barring that, we have to use multiple versions of the story, knowledge of Mande culture and rhetorical devices, and a bit of archaeology to propose particular readings that include various factual and symbolic elements that change over time. There's plenty of criticality and disagreement involved, but it usually remains within a smaller group of people. What you're seeing, I think, is the result of a larger body of critical work done over a longer period of time in a wider variety of fields and concerning more familiar historical accounts. When you get into events that have documentation, we still have significant overturnings and challenges (for example, the famous-to-us mfecane debates of the 1980s/90s in South Africa).

This is my sense of it from sub-Saharan Africa, but it would be interesting to hear what Asianists have to say given the far longer and more active literate past they deal with. One of my comp-lit colleagues suggested that these areas of the world are a "black box" to most people in the industrial north for reasons of language or discipline, so they accept (translated) scholarly consensus on their sources more readily and don't see the deep debates and historiographical battles that wage under that surface.

[edit: accidentally a word]

Hello! I don't exactly have an answer to your question, but I do want to clarify a few things. That is, taking a critical approach to ancient sources does not necessarily mean that we must assume a priori that everything is fiction. In regards to the reliability of the Old Testament histories, Hans M. Barstad has made some pointed observations on methodology that may explain to you how scholars should approach their sources:

When dealing with ancient historiography, our sources will quite often have to be given the benefit of the doubt. Whether we like it or not, the pre-modern, narrative historiography of the Hebrew Bible does not provide us with verifiable historical 'facts'. Since we cannot any longer ask for historical facts the way we used to do, we shall instead have to ask for what is likely (very likely, quite likely, not likely). 'Factual historical truth' must be replaced with 'narrative historical truth', which is related to 'factual truth', but not identical with it. It is, of course, always nice when historical statements are 'validated' by those of other sources. This, however, due to the very accidental nature of our sources, will always be the exception rather than the rule.

However, when reading some of the historiographical literature today one is left with the feeling that some scholars have made up their minds beforehand about the reliability of the historical information which we may find in the Hebrew Bible. Being convinced that they are 'fictitious', they are unwilling to discuss these texts in a scholarly manner. Instead, they waste a lot of energy attempting to prove what they already believe that they know. Others, again, have apparently decided beforehand that more or less everything we find in the Hebrew Bible is 'historically correct'. This other extreme, of course, must be judged as equally incompatible with the ideal of an open, scholarly mind.

To conclude: As a historical source the Hebrew Bible is of the 'same' nature and quality as other ancient Near Eastern literary texts. This has the somewhat drastic consequence that if we renounce the use of the Hebrew Bible on the basis that it is late and fictional, we shall also have to do so with regard to most of the ancient sources. If we do not want to do this, we shall have to accept, for better or for worse, the Hebrew Bible not only as necessary, but also as by far the most important source for our knowledge of the history of Iron Age Palestine. To deny this is not only unduly hypercritical, but it is also based on a positivistic view of history that today is deplorably outdated. [1]

I also wanted to point out that there is a fairly broad consensus that King David was a historical figure, even if the details of his life and the nature of his authority remain a matter of debate. Most scholars agree that the word bytdwd in the first fragment of the ninth-century Tel Dan stele means "House of David"; the same name (bt[d]wd) quite possibly appears in the earlier Mesha stele. Thus, we have evidence (however limited) that David was recognized as the founder of the dynasty that ruled in Judah. The minimalist position still represents the minority as far as I can tell, though some of its more vocal advocates might tell you otherwise. The bibliography on this particular topic is massive of course, but I can list works if you're interested.

Anyhow, my main point is that "Western historiography" (many historians, in fact, now recognize that "the West" is a modern and artificial construct) may not actually be as hypercritical towards its sources as it seems to you. I certainly haven't seen such an intense level of skepticism applied to Greek and Roman sources, at least not regularly. Moreover, even if one does somehow demonstrate that a particular source is completely unreliable as a record of the past, that source still reflects the context in which it was written and can provide a window into its author's time.

:)

[1] Hans M. Barstad, "The Strange Fear of the Bible: Some Reflections on the 'Bibliophobia' in Recent Ancient Israelite Historiography," in Leading Captivity Captive: 'The Exile' as History and Ideology, ed. Lester L. Grabbe (Sheffield: Sheffield Academic Press, 1998), 126f.