I don't know about your statistics but at least here parents killing their children has in reality become drastically less common. It feels differently and we too have had some very high attention cases there parents have killed their kids and there has been a lot of talk, how nowadays this happens. But facts are different. In old times kids got killed by their parents much more often. It just wasn't so public knowledge.
And I have to say that I agree with babies not having babies. Again, I don't know about your situation, but at least here younger teens becoming parents has never been that common. Okay, I live in north, and not only plants and animals but also people are slow to grow and mature around here (I think in average our kids are year or 18 months later in hitting puberty than for example NA Caucasian population, or at least our boys are.) And in old times because of the lack of food we were even later. Hundred years ago 16-year-old girls were just expecting their first menstruation, not their first baby. And because of economical things (highly agrarian economy with most people living in small farms) parents needed to keep their kids home and learning skills long enough for them to survive all the responsibilities. Because of that average first time moms in our society even in old times were more like 23-26-year-old. Nowadays few years older, because our kids start school late, many go for post-graduate degrees (masters tend to be a standard university degree here not baccalaureate) and take gap years and women want to be comfortably working before starting family. I was considered very, very young mother when I got difficult child because I was at my early twenties and hadn't completed my masters degree yet.
Tragedies do happen everywhere, always has, always will, but society should do things to prevent them. And one of the ways would be lowering teen pregnancy numbers (that I have to say you have really, really high compared to other western countries. You have about five times teen mothers compared to for example my country and also double or triple teen abortions. Then again there is not much difference between our countries on when kids start their sex life. You have bit more of those, who start really early but also much more those, who don't start before 18.) Also all kinds of supports and realistic chance to get rid of your kid without killing them would help. I think we have before wondered some very tragic cases here there it has seemed that parent had killed a difficult child and wondered if it was because they were not getting supports etc. That kind of things can prevent at least some of the tragedies. Not all, but some.