Yes, parents can isolate themselves and their children. I guess it does sometimes happen, and of course we wouldn't be aware of it (since we are aware of the HEers who do have contact outside the family, by definition).
But I disagree with the rest of your assertions, thesixteenthtry.
Parents have a legal obligation to ensure that their children are receiving an education suitable to their age, ability, aptitude and any SEN they may have, at school or otherwise.
OFSTED is supposed to be there to ensure that such an education is being received by children whose parents choose to put them into school (although, actually, no parent has ever been prosecuted for putting their child in a school that was failing to meet their needs, although they could be prosecuted for it in theory. Of course the law makers are very careful to make sure that responsibility remains with the parents, because otherwise the State would get sued when children commit bullying related suicide etc etc etc).
A LA is legally entitled to ask a family for information about the home education they are providing. If they do not receive evidence that suggests it is suitable to A,A,A,SEN, the LA can (and do) take the family to court. There ARE legal protections to "stop a parent raising a very deprived child who knows next to nothing".
Yes, parents can have odd agendas. Some of us think the state has a pretty odd agenda in a lot of its pedagogical ideology (yes, Mr Gove, I'm looking at you). We'd rather educate our children in harmony with our own family's values rather than those of a bunch of random people who are teaching in schools. While the family remains the core unit of our culture, what's wrong with that? Home Educators are obliged to "prepare their children for life within the community of which they are part". It's not quite those words but that's the gist. I don't remember whether it's in the law or whether it's in the guidelines for LA's on Elective Home Education. But it is a very good reminder that the State has no business claiming that only one set of values is acceptable within its borders (and I think that part of the legislation was put in to avoid discriminating against Gypsy/Roma people among others)