Common sense gun regulations are part of the solution though.

Australia has 3 firearm murders per 1,000,000 people and the USA has 32.

I don't think that's correlation. That's because firearms are not easy to get in Australia which is part of those reforms. The buyback scheme got 650,000 firearms out of circulation, that has an effect on violent crime.

The murder rate in Australia is 1.3 per 100,000 people and in the US it's 5.

There are obviously a whole lot of factors that contribute to this. The Australian tax rate is really high, and a lot goes into services for mental health and low-income communities, but one of those factors is the inaccessibility of handguns and semi-automatic rifles.

The problem isn't with public schooling per se... it's with the resources that go into low-income areas. Lots of public schools have minimal violence, but when you have entire communities with very little opportunity, then violence increases.

Absolutely agree with your third point. The introduction of abortion laws and the outlawing of lead paint in the US had a significant impact on lowering crime 20 years later. The US is a great case study on this because the different states enacted different laws at different times so you can see the actual causation.

Hopefully reducing neglected children is something that countries and states get better at over time with family planning and health services... but if there are children that are neglected, you definitely don't want them to have easy access to high-powered weapons.