If there was any actual causal connection between the fear and safety sure. Instead it was irrational from both directions of not caring in the past about things like stupidly dangerous 50s toys to freaking out about kids playing in backyards unsupervised.

Ironically safety of children seems to be the complete opposite of the direction of the 'increased safety boosts risk taking'. When children have a higher rate of mortality they tolerate risks more but when there is a lower one they become more paranoid. I suspect the reason why is that most people have a terrible innate sense of statistics and probability - as shown by the success of gambling institutions like Las Vegas and the lotto.