Today, February 5th, is the Safer Internet Day (SID) - "organised by Insafe in February of each year to promote safer and more responsible use of online technology and mobile phones, especially amongst children and young people across the world" (here).
See also "EU: Net Neutrality is about Transparency; Favor of Parental Control" - here and "Deutsche Telekom Group supports Child Online Safety Initiative" - here.
The above statement from DT shows that operators may help parents make the internet safer for children. For example, they may provide network based parental control services. There is even a revenue opportunity associated with the service.
During the years, I covered several such deployments as you may see in the following table (taken from my recent report - "The Broadband Traffic Management 2013 Deployments Directory", available here.