In the Bible, personal identity is not primarily a question of some substance inside a man. But each man still has a nature, inherited from his father. So ontology is not a philosophical problem in the Bible, but rather a problem of generation. And when this generation is sinful, the only solution to the problem is regeneration, which is to say, generation by a new father.
So can we say that God gives exactly the same thing (Himself) to all baptized individuals? And then account for the differences in outcome by saying that God’s Spirit works with all individuals differently? I don’t think so.
When someone gets married, he gives himself. And he does so, promising that he will continue to do so forever. God does the same with His elect. “For I am persuaded, that neither death, nor life, nor angels, nor principalities, nor powers, nor things present, nor things to come, nor height, nor depth, nor any other creature, shall be able to separate us from the love of God, which is in Christ Jesus our Lord” (Rom. 8:38-39).
The elect believe this promise, and it is always fulfilled because the promises are always apprehended by faith. It is not fulfilled for the reprobate covenant member because he does not believe it, and never did. So if God gives Himself to me as my Father, then this means that I no longer have the nature of my first father, the devil. This is why God continues to be a Father to me. If He gave Himself fully to a reprobate covenant member, then He would give Himself the same way tomorrow, and the day after, and suddenly the reprobate covenant member cannot be considered reprobate.
So long as we acknowledge that there are covenant members who are not saved, then we must necessarily say that God does not give Himself to all in the same way. And this is just another way of saying that some covenant members need to be regenerated.