why can't religion reduce the rate of crimes in our society?
Religion as a practice just as you have said does not completely eradicate self and one's nature/attributes. The practice of true religion, just helps to put these attributes under a check. Unfortunately, many do not practice true religion and their true nature that has been set either genetically or environmentally induced, has not been put under check and they only just hide under the the cover of being religious.
This is very clear as the answer speak volume most they way I perceive the question, as long as human being is concerned where what is inside the heart is hidden it's very deficult for any religion to completely cut off crime but can only minimize the rate at which they would have occur through sound teaching and this could only be possible to those who 65% is to practice the true relijion.
Secondly religion don't have any parameters set to measure in how they can cut off crime because it's when you have such parameters that you will check and balance to know if your able to do or not, though people may say that sound religion has the power to cut down crime I don't disagree but can't eliminate it completely based on the human heart difference and the mind construction can't be read by the face many wear religion as cloth and are ready to dropped it at any given time to perpetrate crime.
Just as have said earlier if religion has parameters it's this that will make them know that from so number to next number is crime free and from there they will know what is left to tackle there by achieve it but since no parameters is not possible.