I can imagine that HE would work brilliantly in many, many cases. It might not be ideal in cases where:
the parents themselves do not model curiosity or interest in the world around them
the parents have a very negative attitude towards learning and education
(tbh school is going to struggle too, with the children of parents like this, but I have known cases where an inspiring teacher has made all the difference, despite parental attitudes)
the parents do not find it easy to provide a safe outdoor environment to play in
(notice that the assumption in previous post is that everybody has a detached house with a garden in a safe area)
the parents have a very narrow social circle and the HE groups are either difficult to get to or very similar to family
(very aware that lovely as my own highbrow, keep-ourselves-to-ourselves family and their friends were, I benefitted enormously from meeting completely different people at school; otherwise, I would have found it very difficult to get along with people who weren't just like us)
the parents suffer from social anxiety or other MH issue which makes it difficult for them to take dc out or help them interact with other people
the parents do not have transport and there are no local HE clubs within easy reach
the child does not want to be home-schooled
(this was the case for my dd who had to spend time at home due to health issues and was desperately unhappy)
Of course, most people who are currently HE'ding do not fall in any of those categories. But that would be my objection to seeing HE'ding as something that was right for every family.