The best interests of the children must be the forefront. Home education is a hugely diverse area and the majority of home edders put alot of effort into providing a broad education outside school.
However there are those that really are not able or prepared to put in the effort leaving children to suffer from a poor education.
At worst, a very very small minority use home Ed as way of removing the child from outside interference in order to cover up abuse or neglect. I have participated in a number of child death overview panels involving children deliberately kept away from any form of scrutiny or intervention, leading to very tragic outcomes.
I am not anti home Ed. But I am pro children being protected. A register can only help, even if only a little bit. This is not about what parents want, this is about protecting and supporting children.