Should babies/infants be baptised? The answer depends on whether baptism has some spiritual value. There is no point if it doesn't - for example if baptism is just getting wet, or just a public witness that a person has "accepted Jesus as their personal Lord and Saviour".
But if baptism has spiritual value then it is justified. Indeed Justification is the most important aspect of this.
The Council of Trent defines Justification as "being a translation, from that state wherein man is born a child of the first Adam, to the state of grace, and of the adoption of the sons of God, through the second Adam, Jesus Christ, our Saviour." (sess 6 Chap IV)
According Paul in the letter to the Romans chap 5
12. "Therefore as sin came into the world through one man and death through sin, and so death spread to all men because all men sinned"
Who was this one man? Adam.
Then verse 15-19 spell out the consequences for us all.
15. For if many died through one man's trespass………
16. For the judgment following one trespass brought condemnation, ………….
17. If, because of one man's trespass, death reigned through that one man, …………
18. Then as one man's trespass led to condemnation for all men,………
19. For as by one man's disobedience many were made sinners,……
Adam's sin affected all mankind; it affected our nature and brought death into the world and we became separated from God and subject to condemnation.
"For as in Adam all die, so also in Christ shall all be made alive." (1Cor 15:22).
When we are born we are "in Adam". We need to be "in Christ" because "There is therefore now no condemnation for those who are in Christ Jesus." (Rom 8:1)
Paul says in Eph 2:3 "we [Christians] were by nature children of wrath, like the rest of mankind."
But in Gal 3:25 he says "for in Christ Jesus you are all sons of God"
When we are "in Adam" we are "children of wrath" but when we are "in Christ" we are children of God.
That movement from being "in Adam", subject to death, subject to condemnation, being "children of wrath", to being "in Christ", made alive, brought out of condemnation, being children of God, is effected by baptism.
We are born "in Adam" but to have life we must be "born again", renewed, born by the Spirit in baptism (John 3:5, Ti 3:5).
When we are baptised we "put on" Christ (Gal 3:27); we become part of the body of Christ, and therefore children of God (1Cor 12:13); we become part of a new creation in Christ (2Cor 5:17); we receive the indwelling of the Holy Spirit (Acts 2:38)
Jesus said "Truly, truly, I say to you, unless one is born anew, he cannot see the kingdom of God."(Jn 3:5) and yet he also says "Let the children come to me, and do not hinder them; for to such belongs the kingdom of heaven." (Mt 19:14)
All this is good and necessary for adults. All this is equally good and necessary for children.
As the Bible says "For the promise is to you and to your children and to all that are far off, every one whom the Lord our God calls to him." (Acts 2:39).