Why did Christ found a Church?
What purpose does the Church serve in the economy of salvation?
I understand it in a similar way as if you were to ask 'why did God create the institution of 'family'?
Second only to Church, is the family regarded as a sacred institution. Why then did Jesus say such as thing as 'you are all My mothers and my brothers' ? It certainly wasn't so that we'd deconstruct this important institution of family. I understand Him to have opened the way for the special relationships that thrive in the nucleus that is family, to be applied by us in all the relationships that tie humanity together.
What does the family serve in the economy of salvation? It is the sacred nucleus that guards the integrity of humanity now and for generations to come.
The common good of the perfect society which is the Church is God Himself. Not relationships that tie together humanity. The common good of the imperfect society which is the family is, in the context of sacramental marriage, ordered to the common good of the Church, to educate and build the faithful. The family is indeed a fundamental natural institution (though as such it is by definition not sacred, though as ordered to God as a sacrament it has a sacred element ). But I see nothing of help here, and certainly nothing along the lines pax is thinking of.