Yes, I agree that there are children who have mental health issues who are no longer attending a school. And some who have been failed by local authorities in regards to EHCP provision or other duties.
Nobody knows how many because there hasn't been a national system of monitoring and checks to ascertain why - and if nobody knows who, where or why, nobody can help - whether that is by providing alternative education, MH support, family support, obtaining EHCPs or ticking off a box to say the child is receiving a great education from an engaged and proactive parent - if nobody looks, nobody can say why or how many are.
The data gathering could actually provide evidence to inform and support better approaches towards educating and safeguarding children such as those - without good data, it's like blaming cholera on bad luck because there's no evidence to suggest that there's a problem with a particular area's water supply because nobody's looked so can't see geographical distribution.
There are also children who have either been withdrawn from school under the guise of elective home education or were not enrolled in the first place for the benefit of an abuser. And children who aren't actually in the country anymore, whether happy with family, trafficked, infibulated, forced into marriage or, frankly, dead.
It's not safe to continue to shrug our shoulders and say 'well, I'm sure the parent is doing a grand job, even though we don't even know for certain if the child is there. Abusers, radicalised people and some who just can't parent or educate effectively also claim to be home educating. This won't solve everything, but if it flags up a few children who are in danger from someone in their household, that's lives saved.