Parents can give salvation to their children? Gotta verse for that? And baptism vs healing are two completely different things. Yes people can be healed on the faith of someone else. But there isn't a single verse suggesting an infant that cannot hear or comprehend or accept the gospel can be saved by the 'faith' of the parents. Youre reading that into the text. Its called eisegesis.The bible states whole households were baptized.
Through the faith of another one can be healed.
excluding the faith of a parent to give the free grace of salvation to their children is purely arbitrary on the NC part.