the only reason that any secrets are revealed in the confessional is that the sinner wants his soul to get to heaven because of what he did as he seeks forgiveness and absolution.
Make it so the police are the third party in the confessional and you've removed much of the reason that the police don't act as confessors.
It's the same with counselors. If you go to a psychiatrist and say, "Doctor, I want to get better" and confess to a crime, you're turned in. Why would a sane person go to a psychiatrist?
It's different with secular priests called "lawyers," to whom those who committed crimes go and say, "Hey, I did nothing wrong." It's possible to confess and make a lawyer into a mandatory reporter, but most lawyers will make that confession go away and seek absolution in the denial of wrong doing. Then the lawyer will do everything possible to get somebody declared not guilty, even if the lawyer has a decent suspicion that the client really is did the crime. Suspicion isn't proof.
Society has layers. There's the official, government layer, with law enforcement to enforce the secular, official moral code. Then there's a set of civil society layers, to enforce a similar, but distinct, code. Then there's layers based on kin groups, enforcing yet a different, presumably non-conflicting, code. American society, given it's atomism, seems to be trending towards there just being an official code.