No, a baptism isn't supposed to magically become a Christian, any more than an adult is supposed to magically stay a Christian. Baptism is a sacrament of initiation where the purpose is to live freely as a child of God rather than remain entrapped in the slavery of sin. The baptized receives the gift of the Holy Spirit.
I was baptized as an infant, and though I miss not remembering the event, I can look back to as early as age three and note where the Holy Spirit was working in my life.
Indeed, the Catholic Church does go by the true purpose of Baptism which is for the remission of sins, rebirth into the family of God, and to receive the gift of graces and the gift of the Holy Spirit. That spark of faith that is within everyone's heart receives an early start. Catholics believe in all sacraments there are visible signs of the invisible reality. With baptism, we simply acknowledge this invisible reality early.
Some are concerned about the remission of sin part. How can a baby with no personal sin receive remission of sins? Same way as an adult who sins after baptism. Sin, meet baptism. Baptism isn't merely a one time only event. It seals us with the spiritual mark of belonging to the family of God, and that seal is everlasting.