Well, I'll refrain from giving my opinion on the issue, since personal opinions are worthless.
The Church, however, considered "illegitimacy" to be an impediment to the priesthood, at least until Vatican II (which is what most Trads go by). So without special permission, men born outside of a lawful marriage could not become priests. The priestly candidate needed an actual dispensation if he was illegitimate (The Latin "spure" in used in by the Church, which translates "spurious" or "bastard").
The Church seems to think that they are, in some way, damaged goods. Regardless of whose fault it is.
Keep in mind that God clearly intended for children to have both a father and a mother in their education and upbringing. Take the father, for example. The father actually stands in for God Himself, teaching the children indirectly what God is like. Is he strong? wise? loving? just? fair? overly strict? unreasonable? always angry? violent? absent?
They can't see God, but they can see their father. Their concept of Authority, Fatherhood, God, etc. all comes from what they observe in their father. It's a grave responsibility!