Yeah, that article about ignoring minor crimes sure is convincing with regard to homicide. Clearly if police stopped investigating homicides, they'd actually go down.
Fairness where it's due, given the nature of most homicides, it's fairly likely they wouldn't
increase much. Consideration of those sorts of consequences don't tend to really play into the decision-making involved with most of 'em, so the preventative effect of investigation probably isn't actually particularly large.
Cops no longer casually killing people isn't quite equivalent to stopping investigations, though. If it was associated with a general reduction in police abuses it probably
would have good odds of reducing homicide, by sheer dint of the societal benefits that would start sprouting up if cops stopped regularly abusing communities. That'd take a lot of serious fucking reform, though.