I completely agree there should be more oversight, but I don't think there is either enough will politically even with this horrific case that home educators are likely to have to accept it yet & I don't think Education Welfare as it stands now is in a place to do it. We've seen during the Badman review that the loudest home educators will rally against oversight, spread fearmongering to keep people from supporting it (during that, there were instances of slippery slope reporting, claiming thing like that government officials wanted to require intimate physicals on home educated children to check for abuse, which was reported in some home ed groups as fact), and there isn't really much of a void of the middle ground.
The data I've seen strongly suggests that home education in itself isn't a safeguarding concern, but becomes one when it is combined with other safeguarding concerns. Pulling children to home educate when there are already safeguarding referrals should be a red claxons.
In my dreams, home educators would register the same as school educated parents, and each academic year at least would have a meeting outside the home for the parent and child to show progress, discuss concerns and ways to support the child and family's needs, with independent career/qualification guidance for teenagers.
I home educated my children for over 15 years, I had no oversight for over half of that time and barely any when I did. I cancelled one home visit due to a family funeral and just fell off the radar. I have seen far too many of my children's home educated peers get into bad situations that would likely have had more support in school. Once our home ed kids get to a certain age, they're basically invisible. No one checks when a parent signs off at 16 that a child is still being home education whether that child is actually getting that.
I've also sat on a school governing board and been in Chair and Vice Chair briefings with the local authority, hearing the head of Education Welfare complain about the rise in home education in our area & nationally, read out snippets of emails from parents who had withdrawn a child to home educate who were, to me, clearly in distress (and one very clearly confusing Elective Home Education with Education Otherwise Than At School), infer the parents were idiots and called all home educating parents arrogant.
So yeah, there are reasons why home educators are resistant to oversight - most home educated children in the UK are withdrawn after an issue in school, and even children who were home educated from there start, many of the parents have had some sort of issue with public services who have a dim view of parents. The children deserve better, but I don't see how to get there with how things are now and have been for such a long time.