The norms of the Roman Missal state that, While the Priest is receiving the Sacrament, the Communion Chant is begun, its purpose being to express the spiritual union of the communicants by means of the unity of their voices, to show gladness of heart, and to bring out more clearly the “communitarian” character of the procession to receive the Eucharist. The singing is prolonged for as long as the Sacrament is being administered to the faithful…. (GIRM # 86). The instructions also state: When the distribution of Communion is over, if appropriate, the Priest and faithful pray quietly for some time. If desired, a Psalm or other canticle of praise or a hymn may also be sung by the whole congregation. (# 88).
 
Note then the emphasis on the “communitarian” nature of this moment. And while private prayer is not wholly excluded, neither is it extolled as the main point or purpose to be pursued at the time of receiving Holy Communion.
 
The Sacred Liturgy is fundamentally a public and corporate act of worship of the whole Body of Christ together. It is not essentially a private devotion. The norms do permit a time after communion for silent prayer, if this seems appropriate. The length of such time and the use of this option will vary depending on the needs of the congregation and other factors.
 
Your concerns are understandable, but they need to be balanced with what the Church teaches us about what the Liturgy most fundamentally is. Consider that in the first Mass, at the Last Supper, the Apostles did not go off and have private conversations with Jesus. Rather, they experienced him corporately, and the Scripture says, that after partaking of the Sacrament, they “sang a hymn” (Mt 26:30). If we extend the first Mass to the foot of the Cross, there too, those that made it that far, stayed together and supported the Lord and each other.
 
Private prayer and Eucharistic devotion are to be encouraged, but, there is a context where this is best. Public prayer is also good and to be encouraged. It too has a context that should be respected for what it is.

You are correct. Modern and very helpful devices such as the enumeration of chapters and verses are not part of the original biblical text. These helpful conventions were added much later.
 
The setting of the biblical text into chapters occurred in the 13th century when the Catholic Archbishop of Canterbury, Stephen Langton assigned chapter numbers in order to make the reading of the Bible easier. The enumeration of the text into verses did not happen until 1551 when Robert Stephanus, a Protestant, former Catholic, classical scholar and also a printer, published the first such Bible in Paris.