There are several lines of thought to it. One is that if the killers don’t get their manifesto out themselves then don’t promote it because it would likely inspire copycats. Same idea as not making these (fame-seeking) killers famous.
About the only times I’ve agreed with releasing a manifesto or behind the scenes coms with police are something like the Unabomber or Zodiac killer to catch who did it.
I used to think these were interesting to read, but there are no doubt cases where it inspires others. A lot of them release it to multiple places like Elliot Rogers and build up to it, so it gets archived. If they’re going to release something not already public like this, I’d say at least wait 10 years or more so it’s more a historical record than any matter of pride.