To your first point: there should be a term because it is clearly a useful idea that people want to communicate. The ambiguity or inelegance of what current exists to express the idea means we should at least desire a better way of expressing it - that is, a term for it.

To your second point: "son" or "daughter" is not sufficiently general, and it is gendered. What if I wanted to express the idea of adult offspring without knowing (or caring about) the gender of that person?