Clear proof that the majority of parents have neither the effort, the energy, nor the inclination to pay attention to what their children do while on their phone, to the extent of losing thousands of pounds of money (or in some cases, hundreds of thousands of pounds)

and,

the children's ability to access porn through their parent's mobile phone over a phone network,

are unrelated?

That doesn't seem the case to me. In my experience, even very innocent searches can (unfortunately, and unexpectedly) bring up porn-related material.