Second, in my own private interpretation, I don’t think that it’s on the basis of the parents’ faith that the infant receives the regeneration of the water and the Holy Spirit. When the catechism says that “Christian parents will recognize that this practice * also accords with their role as nurturers of the life that God has entrusted to them,” I read this rather as saying that the infant can be baptised, chrismated, and brought into full communion with the Church by virtue of the fact that the infant Is now in the ecclesia domestica that his or her parents provide for the nurturance of the child’s faith so that his or her nascent faith won’t be later shipwrecked.
But you can’t be shipwrecked if you aren’t first out to sea, so when I was myself a catechumen ten years in the Church preparing for my own baptism, I was taught that infants are admitted to the Holy Eucharist by virtue of their own faith in a sense, because faith is a mystical thing. Infants indeed have faith according to what I’ve been taught in my own Eastern Catholic tradition, though not a rational or self-reflective faith (like faith is often thought of in the West). When the curse is made null for them they are restored to the state of Adam and Eve before the fall: only this time, unlike the old Adam and Eve, they now have an opportunity to grow to maturity and reach perfection surrounded by a supportive community and with access to the Holy Mysteries with God himself dwelling in them.
Perhaps this is a different perspective just in the Eastern quarters of the Catholic Church. I once heard that in the Latin West it is believed that Adam and Eve were already perfect or mature before the fall. In the East, we usually think of them as spiritual infants.*
I like your description, but one thing I would like to add; expounding on the old vaccination analogy, when we bring our children for vaccinations it is not we that cure them but rather the vaccine within them; so likewise, it is the miracle of God’s saving grace that works within the child (or adult) in baptism. The child neither understands nor can reflect on their immunity in either case.