Tautologically, each student at a university who is a blood relative of a graduate of said university has a social network that shares a node with the university's formal network.

"Social capital" is a term of art in sociology meaning "the network of relationships within a particular society", in this case a university. Robert Putnam has written extensively about the empirical benefits of high social capital, which include efficient allocation of resources, lower stress, and prosocial behavior.

A newly admitted student whose social network shares 0 nodes with the university's formal network makes no initial contribution to the university's social connectedness within the universe of people formally affiliated with the university. Whereas the legacy student is already socially connected at the moment of admission.

If you think your society is better than average, you want to continue its culture.

If you shred cultural continuity mechanisms, eg legacy admissions forming a persistent community, you erode the very thing that made your society better than average.