Thanks PinkyU, but that's not really what I was asking. (And in any case, it has not been my experience that school caters for average cognitive development only, despite the fact that my dd is an academic "outlier", but I accept that this will depend on the school.)
My question was not about the benefits of HE, which are fairly obvious, but more about how you can evaluate its effectiveness. In the school system, this is a responsibility that is shared by many people, including parents, teachers, school leaders, governors, external inspectors and a multitude of other stakeholders, so there are lots of checks and balances in place. I can't see any of those checks and balances in place for an HE set-up, so I wonder how parents can be sure that they're doing a good job and meeting all of their child's needs without that breadth of perspectives and shared responsibility.
That's not to say that some HE parents aren't doing a fantastic job of providing a well-rounded education for their children - I'm sure that they are in some cases - but I'm not clear on how they know that this is the case, or on who would hold them to account for any areas in which the quality of education might be lacking.