OP, I think you have misunderstood why schools being such high risk settings for Covid transmission is such an issue for some families that they have chosen to de-register students rather than send their children back into school.
- Some children have been instructed by their own paediatricians that they must still isolate. This presents a problem for e.g. siblings - parents, ime, have generally been able to make arrangements with understanding employers to wfh in the light of their child's extreme vulnerability, but siblings are still expected in school. Families may deregister all children to protect the extremely vulnerable child.
- Some families similarly have CEV adults - parents, other carers such as grandparents - living in the family, which creates the same issue.
- Some families have a family member undergoing or, worse, waiting for critical treatment. Hanging on a waiting list for surgery is bad enough, without also knowing that if you test positive for Covid, your months / years delayed slot will be given to someone else - again, i know of families where a parent reluctantly keeps a child at home for quite long periods because an operation before which the family has had to isolate is repeatedly cancelled.
Even for those families that decide to send children into school despite the risks it poses to CEV adults - the mental and emotional strain on the children can be enormous, can lead to school refusal, and as I have repeatedly said, the fact that CAMHS is completely overwhelmed and has a 2 year+ waiting list means that there is no support.
It is also worth noting that the alternative course of action that you are now proposing - that every school [I presume you actually mean 'every service that works with children - so including social services, all therapists, Ed Psychs, family support workers etc etc] should have remained fully open to all children and families throughout the entire pandemic, despite transmission risks - also came with significant downsides. We, as I am sure all other schools do as well, have newly-vulnerable children due to the death or serious Covid-related illness of parents or carers. In our case, these occurred when the schools were open - late 2020, mid 2021 delta wave - and in at least 1 case can be linked to children bringing the virus home. That's not damage-free for children either.
Should the country be able to identify where its children are, and provide all the support services they need, whether in school or in other services? Absolutely, and this has always been the case.
Are there 100,000 'lost' children? No.