It doesn't always give an advantage though, sometimes it just creates an almost level playing field.
My parents could just about afford to send my brother private on a subsidised place, through my mum working nights (at higher pay) then sleeping whilst we were at school, she got used to existing on about 5 hours sleep. My brother was refused any help or any diagnosis as a child, but absolutely could not cope in mainstream, he came home most days with cuts and bruises from being attacked in his main stream school. When he came home with a broken eye socket, my parents decided enough was enough and moved him to a small private where he could cope. He came out with C's and D's in his GCSE's, but most importantly he came out with his mental health just about intact, no longer suicidal.
I went to a 'sink school' for secondary, there was no teaching, just crowd control. I taught myself the curriculum from study guides and got through with no issues by giving the 'cool kids' the answers in lessons, the teachers were too busy breaking up fights to notice. I came out with all A's at gsce and a levels and an offer to study medicine at Cambridge.
Ultimately, for all this talk of equality, life is not and will never be equal. Some children are born with disabilities, some are not, some have supportive parents, some don't,some are brighter and more motivated.
If your children are limited, it is only by their abilities and attitudes and those of the people around them. I could have been all 'poor me, it's so unfair that my brother is getting a different education to me, if i cant have it then no one else should either'. Or I could make a choice to take control over my future myself, and I count myself much more fortunate than my privately educated brother.