Are you saying, cat64, that the best way to ensure that all children are safe and well is to ensure that they are all seen by "child professionals"? Shoud every child have regular safe and well checks, or only the ones who do not come unto contact with state-employed and state-trained child professionals on a regular basis through state school, NHS or similar?
If children are at private schools, or seen by private health practitioners, or members of some sort of community group (guides, church, ballet/music classes, whatever) is that sufficient for safeguarding purposes?
I'm all in favour of living in a society where we care for others and offer support, I'm less in favour of living in a society where the right to private family life is bulldozed because of some idea that a safe and well check will prevent child abuse. I need more evidence that such checks do more good than harm before being happy to give up a fundamental civil liberty.
As for your last question:
"disappears off the radar" presumably suggests that a family has been on the radar previously, yes? If a vulnerable family has come to the notice of the authorities, and there is good reason to think that the family is at risk, and then they move without notice, then yes, of course Children's Services should be making sure all is well if they possibly can. But if there is no reason for Children's Services to think that anything is wrong beyond the fact that a family chooses to live without using State-employed teachers, doctors, dentists, whoever, then yes, they should leave the family alone to go about their lawful business.
I think it is often easy for those in Children's Services to forget how much harm they do simply by investigating and invading the lives of innocent families.