I don't really have any negatives about HE, as such. I haven't HE'd, but we lived for 5 years in an intentional community where most children historically had been HE, so I've known quite a lot of HE children both in the community and others who visited.
I sent my dd to school when she reached reception age because it felt like the best thing for us, and because her closest friend in the community went to school.
One thing I would say, which is kind of hard to put into words, is that there was much less 'equality of outcome' amongst the children than you would expect from a group HE'd together. That is - the children whose parents had an Oxbridge degree/whatever, ended up going off to uni or something similar, whereas the children whose parents had a lower level of education went to the local college to study catering, hairdressing etc.
As I say, its not really a negative, because unfortunately that is very much what our society is like, and I don't think that things would have been different if the children concerned had gone to school, but I might have expected a less 'predictable' outcome.
Overall, I would say there are children who get a great education through HE, and others who get a pretty rotten one. But, frankly, that is exactly true of children in school.