If only water is the only purpose in Baptism
The oil is not necessary for a valid baptism, that’s true. The oil is to anoint the person, joined to the body of Christ through baptism, as king, prophet, and priest
The oil of catechumens (pure olive oil) can accompany a minor exorcism prayer prior to baptism.
Before they are baptized, infants often are anointed with the oil of catechumens to prepare them for the waters of baptism. It is a minor exorcism that clears any unholy spirits so that the Holy Spirit may fill the child. Oil also is seen as strengthening.
Immediately after baptising an infant, a series of explanatory rites highlight aspects of baptism. An anointing with Chrism recalls the anointing of prophets, priests and kings in ancient Israel. Our own participation In this anointing shows that we too share in those offices as members of “a royal nation, and a priestly people” by becoming a part of the Church. Other explanatory rites include receive a candle as the light of Christ, a white garment to show purity after being cleansed by the waters, etc.
For adults, the anointing with Chrism after baptism is the sacrament of Confirmation. It represents the gifts of the Holy Spirit that we receive. Chrism has been consecrated by the bishop as a sign that these gifts are recognized by the whole church, by all who are in communion with the bishop.
This. Also one of the properties of oil is that it’s absorbent so, when it was blessed, it absorbed that holiness which in turn is absorbed into the one anointed with the oil.
I assume the post-baptismal anointing with chrism is actually a remnant of the ancient practice of in mediating confirming infants after baptism… as still practiced in the East.