It also ignores that the major function of these services was to baptize catechumens, which was done during the Old Testament lessons
The catechumens are indeed baptised in the Easter Vigil. It comes a little later in the mass.
THE BAPTISMAL LITURGY
When there is a baptism
After the Homily the Baptismal Liturgy begins. The Priest goes with the ministers to the baptismal font, if this can be seen by the faithful. Otherwise a vessel with water is placed in the sanctuary.
Catechumens, if there are any, are called forward and presented by their godparents in front of the assembled Church or, if they are small children, are carried by their parents and godparents.
Then, if there is to be a procession to the baptistery or to the font, it forms immediately. A minister with the paschal candle leads off, and those to be baptized follow him with their godparents, then the ministers, the Deacon, and the Priest. During the procession, the Litany is sung. When the Litany is completed, the Priest addresses the people.
If, however, the Baptismal Liturgy takes place in the sanctuary, the Priest addresses the people first, in these or similar words, and the Litany follows.
If there are candidates to be baptized:
Dearly beloved,
with one heart and one soul, let us by our prayers
come to the aid of these our brothers and sisters in their blessed hope,
so that, as they approach the font of rebirth,
the almighty Father may bestow on them
all his merciful help.
If the font is to be blessed, but no one is to be baptized:
Dearly beloved,
let us humbly invoke upon this font
the grace of God the almighty Father,
that those who from it are born anew
may be numbered among the children of adoption in Christ.
The Litany
The Litany is sung by two cantors, with all standing (because it is Easter Time) and responding. In the Litany the names of some Saints may be added, especially the Titular Saint of the church and the Patron Saints of the place and of those to be baptized.
Lord, have mercy.
– Lord, have mercy.
Christ, have mercy.
– Christ, have mercy.
Lord, have mercy.
– Lord, have mercy.
Holy Mary, Mother of God,
– pray for us.
Saint Michael,
– pray for us.
Holy Angels of God,
– pray for us.
Saint John the Baptist,
– pray for us.
Saint Joseph,
– pray for us.
Saint Peter and Saint Paul,
– pray for us.
Saint Andrew,
– pray for us.
Saint John,
– pray for us.
Saint Mary Magdalene,
– pray for us.
Saint Stephen,
– pray for us.
Saint Ignatius of Antioch,
– pray for us.
Saint Laurence,
– pray for us.
Saint Perpetua and Saint Felicity,
– pray for us.
Saint Agnes,
– pray for us.
Saint Gregory,
– pray for us.
Saint Augustine,
– pray for us.
Saint Athanasius,
– pray for us.
Saint Basil,
– pray for us.
Saint Martin,
– pray for us.
Saint Benedict,
– pray for us.
Saint Francis and Saint Dominic,
– pray for us.
Saint Francis Xavier,
– pray for us.
Saint John Vianney,
– pray for us.
Saint Catherine of Siena,
– pray for us.
Saint Teresa of Jesus,
– pray for us.
All holy men and women, Saints of God,
– pray for us.
Lord, be merciful:
– Lord, deliver us, we pray.
From all evil,
– Lord, deliver us, we pray.
From every sin,
– Lord, deliver us, we pray.
From everlasting death,
– Lord, deliver us, we pray.
By your Incarnation,
– Lord, deliver us, we pray.
By your Death and Resurrection,
– Lord, deliver us, we pray.
By the out-pouring of the Holy Spirit,
– Lord, deliver us, we pray.
Be merciful to us sinners:
– Lord, we ask you to hear our prayer.
If there are candidates to be baptized:
Bring these chosen ones to new birth through the grace of Baptism:
– Lord, we ask you, hear our prayer.
If there is no one to be baptized:
Make this font holy by your grace for the new birth of your children:
– Lord, we ask you, hear our prayer.
Jesus, Son of the living God,
– Lord, we ask you, hear our prayer.
Christ, hear us.
– Christ, hear us.
Christ, graciously hear us.
– Christ, graciously hear us.
If there are candidates to be baptized, the Priest, with hands extended, says the following prayer:
Almighty, ever-living God,
be present by the mysteries of your great love
and send forth the spirit of adoption
to create the new peoples
brought to birth for you in the font of Baptism,
so that what is to be carried out by our humble service
may be brought to fulfilment by your mighty power.
Through Christ our Lord.
Amen.
The Blessing of Water
The Priest then blesses the baptismal water, saying the following prayer with hands extended:
O God, who by invisible power
accomplish a wondrous effect
through sacramental signs
and who in many ways have prepared water, your creation,
to show forth the grace of Baptism;
O God, whose Spirit
in the first moments of the world’s creation
hovered over the waters,
so that the very substance of water
would even then take to itself the power to sanctify;
O God, who by the outpouring of the flood
foreshadowed regeneration,
so that from the mystery of one and the same element of water
would come an end to vice and a beginning of virtue;
O God, who caused the children of Abraham
to pass dry-shod through the Red Sea,
so that the chosen people,
set free from slavery to Pharaoh,
would prefigure the people of the baptized;
O God, whose Son,
baptized by John in the waters of the Jordan,
was anointed with the Holy Spirit,
and, as he hung upon the Cross,
gave forth water from his side along with blood,
and after his Resurrection, commanded his disciples:
“Go forth, teach all nations, baptizing them
in the name of the Father and of the Son and of the Holy Spirit,”
look now, we pray, upon the face of your Church
and graciously unseal for her the fountain of Baptism.
May this water receive by the Holy Spirit
the grace of your Only Begotten Son,
so that human nature, created in your image
and washed clean through the Sacrament of Baptism
from all the squalor of the life of old,
may be found worthy to rise to the life of newborn children
through water and the Holy Spirit.
If appropriate, he lowers the paschal candle into the water either once or three times as he continues:
May the power of the Holy Spirit,
O Lord, we pray,
come down through your Son
into the fullness of this font,
Holding the candle in the water, he continues:
so that all who have been buried with Christ
by Baptism into death
may rise again to life with him.
Who lives and reigns with you in the unity of the Holy Spirit,
one God, for ever and ever.
Amen.
Then the candle is lifted out of the water, as the people acclaim:
Springs of water, bless the Lord;
praise and exalt him above all for ever.
After the blessing of baptismal water and the acclamation of the people, the baptism or baptisms take place.
The Renewal of Baptismal Promises
All stand, holding lighted candles in their hands, and renew the promise of baptismal faith, unless this has already been done together with those to be baptized.
The Priest addresses the faithful in these or similar words:
Dear brethren (brothers and sisters), through the Paschal Mystery
we have been buried with Christ in Baptism,
so that we may walk with him in newness of life.
And so, now that our Lenten observance is concluded,
let us renew the promises of Holy Baptism,
by which we once renounced Satan and his works
and promised to serve God in the holy catholic Church.
And so I ask you:
Do you renounce Satan?
I do.
And all his works?
I do.
And all his empty show?
I do.
Or:
Do you renounce sin,
so as to live in the freedom of the children of God?
I do.
Do you renounce the lure of evil,
so that sin may have no mastery over you?
I do.
Do you renounce Satan,
the author and prince of sin?
I do.
Then the Priest continues:
Do you believe in God,
the Father almighty,
Creator of heaven and earth?
I do.
Do you believe in Jesus Christ, his only Son, our Lord,
who was born of the Virgin Mary,
suffered death and was buried,
rose again from the dead
and is seated at the right hand of the Father?
I do.
Do you believe in the Holy Spirit,
the holy catholic Church,
the communion of saints,
the forgiveness of sins,
the resurrection of the body,
and life everlasting?
I do.
And may almighty God, the Father of our Lord Jesus Christ,
who has given us new birth by water and the Holy Spirit
and bestowed on us forgiveness of our sins,
keep us by his grace,
in Christ Jesus our Lord,
for eternal life.
Amen.
The Priest sprinkles the people with the blessed water, while all sing:
I saw water flowing from the Temple,
from its right-hand side, alleluia;
and all to whom this water came were saved
and shall say: Alleluia, alleluia.
Another chant that is baptismal in character may also be sung.