I feel like home education can be a vanity project for some parents, who believe that they can do a better job than people with two degrees in their subject (subject specific and pgce).
The thing is, while many teachers do do a very good job for many children, some do not - this can either be due to the specific teacher, or possibly more commonly because of the teaching context at the moment (target driven, high stakes testing and high stakes accountability measures, decreasing money - as well as a longstanding policy of integrating SEN children in mainstream rather than providing additional Special School places).
I would say that, in the vast majority of cases, non SEN children are likely to do adequately well in school, taught by professional teachers. Some of these might do marginally better if taught by the very best home educators, but to counterbalance that, some would do worse if taught be slightly less expert HEers.
However, many SEN children - particularly those with ASD spectrum conditions, where the institutional nature of school and its sheer number of people and stimuli contribute to their discomfort - do not do adequately well in schools as they are at the moment, or at least do not do adequately well with all teachers in all schools. It is for those children that I feel- as a teacher as well as an ex home educator - that home education (specifically, in many cases, the home environment and the known adult, rather than the educational expertise of the parent) can be a much more positive educational process than school.