In "By the Waters of Babylon" name two ways John acquires power (not just because he is the priest's son),
First of all, he has the courage to go places that no one else has gone before. Being a priest's son doesn't allow him to break taboos that are against travelling in certain areas; however, John feels that he has been given some sort of permission from above to do just that, so he does. He travels further into the land that is forbidden. He breaks the rules, takes the laws of their people into his own hands, because he feels that "if I did not go, I could never be at peace with my spirit again". It is that decision that gives him great power because it leads to his final discovery.
And then in the end, the most significant way that he gains power is that he comes home armed with knowledge that none of his people have. He has been to the place of the God, and knows that "they had been men, neither gods nor demons." He comes home with this knowledge, and it gives him incredible power because it allows them to "build again", to try to interpret the books, to figure out what happened, and to start an entirely new journey.