Which brings me to the other main reason: Calling these stories "chestnuts" is being rather kind to them. One of the commenters refers to them as "just so stories", or "urban myths". They circulate as a kind of liturgical glurge to pad out inadequate exegesis.
I don't oppose them entirely. A good illustration is a powerful thing to engage the hearer. But scripture comes first; the teaching of tradition comes next; the preacher's insight after that. The stories are a condiment, a seasoning, to spice the story, not to overly sweeten it or substitute for spiritual meat.