Did Holmes profit from giving credit to the police?

Holmes profited from giving credit to the police because it gave him greater movement while working, and it enabled him to garner information that was already known by the police...... but also information that was not available to the public. Holmes' clients would not be privy to that type of information when consulting Holmes. In essence, it comes down to the old saying, "lone hand washes the other". If Holmes never gave credit to the police, they would have seen him as an adversary.