Good investigators withhold details about a crime from the public mostly to filter out false confessions. This speaks to the fact that false confessions are common enough to make filtering techniques common practice.
That's not the only goal. This also reduces the effectiveness of copycat crimes, and differentiates any would-be copycats from the original. Also, it enhances the ability of authorities to receive and authenticate tips from the general public. In fact, in a high-profile case, it's common practice to deliberately plant misinformation in the form of slight immaterial errors, for many of the same purposes.
