I don't believe people keep their kids 'safer' because they think the world has become more dangerous.

It's slightly taboo, but I think people protect their kids more now because they are more precious to the parents. The average number of children per mother has plunged in the last 200 years, and investment required in them per child to get them to child-bearing capability is much higher also. Child mortality has dropped like a stone, so any harm coming to children is much less tolerable.

Parents have so much invested in their children - and so few of them to "spare" - that they get far more protection than before.