Well, in a sense we perhaps do. However, I'd label my method as hybrid because I do have a familiarity with at least the Eastern Orthodox treatment of both Gensis and the Bible as a whole. I am at least open to looking beyond the traditional Western enlightenment brand of thought. For example, I don't view Genesis as a scientific account of creation.
The problem I have with what you're saying here is that it's essentially anachronistic. The Early Church Fathers, for instance, held in majority and rather clearly that Adam and Eve were literal. The Apostles and writers of the NT at least held to the same notion, and I would cite passages such as where Jude talks about Enoch (7th descendant of Adam) and Paul cites the first man Adam. They may not have had the culture war battles we do over things, but this was an assumed truth. (There is an excellent article book review
here that backs up this assertion, as I am not just pulling this out of thin air or following traditional talking points with no scholarship.) As such, traditionally there has been a distinguishing between true (substitute literal if you must, but that's not the best word here) story and something more along the lines of a parable or folktale.
The concept of relative truth is a postmodern device (and just as Western in orientation), and that is essentially what is at play here. Please correct me if I am wrong, but the idea you advocate is that the story is essentially a parable, true in the sense that it conveys true ideas, but fable in the sense that Adam and Eve were not actual people who lived, sinned, and died?
I don't know about that; my argument would be that the collective text known as the Bible necessitates that it be true. For example, the first man Adam being a literary construct diminishes the last Adam title given to Jesus (I Corinthians 15:45). If you read the former allegorically, then why does the latter need to be real in order to work.
I am, actually, quite fine with ambiguity, but there are times when ambiguity may destroy things, especially if that ambiguity is constructed in a place where authorial intent was not such.