It is also about opinions on college utility. Do parents think college is a waste of time? If parents think it is waste of time, you are more likely to think the same and drop out.
I think that's part of it, but I think its also about the ability to actually have an informed discussion about what college is and isn't, about what you need to do to be ready for college, and about dealing with problems that arise while in college.
Parents having actual directly relevant experience seems intuitively to be quite likely to have value there.