There are decades old papers [0] on this subject that explicitly use humans as a analogy and call it "reproduction" because of the need to learn or evolve for local conditions. I don't think using terms in a way they've been used since the first serious analysis of the concept is going to confuse anyone.

    I think it's pretty extreme to imagine their nth descendants caring about the goals of the parent civilization.

It's an example to demonstrate the concept in familiar terms, not a psychohistorical prediction.

[0] https://www.rfreitas.com/Astro/ReproJBISJuly1980.htm