Actually, the numbers support religious people committing crimes at higher rates than non-religious. So statistically, it doesn't work "just as well".
If your answer—which appears to be a gross misunderstanding of my comment—is in fact a sincere misunderstanding and if such is due to my failure to communicate effectively, then I offer you my sincere apologies.
I’ll put it another way.
Freud attempted to discredit religious belief by explaining it as “wish fulfillment.” Freud’s ideas are the source of atheist thinking on a popular level.
But Freud apparently never recognized that atheists also have a very strong psychological motive to wish away God’s existence—the freedom to pursue erotic and other material pleasures unrestrained by a transcendent moral law giver.
This is a sound refutation of Freud’s attempt to discredit religious belief, thus eliminating the philosophical groundwork underlying comments such as those in post #266.