I think you may not have a complete understanding of sin. Sin is the choice to do what is wrong. Children and the mentally deficient lack the capacity to fully understand right and wrong and the consequences of their choices. That's why we don't imprison the insane.
Yes, I do believe in an age of accountability. It was I that had made mention thereof. That does not mean that children don't sin, but that their sins are not held against them. That is a significant difference.