I certainly know why I pay- it is because my extremely intelligent son was failing academically in the state system at 6, and was diagnosed with various personality and mental disorders (one decided he was probably autistic at 4 because he preferred sitting in with his anatomy textbook to going out to play football) by the four infant school teachers he came in contact with in his first three years at school. I wanted to find a school that would be a better fit, or at least make some attempt to accommodate him or even make him feel accepted for for what he was.
Since the age of 7, he has attended: a high achieving prep school (moderately good choice, although a little restrictive for him), a state school in Canada (big success), a really laid back independent prep (very, very big success), and an independent secondary (very successful, he is predicted mostly A and A* at GCSE this year). When I think back to the withdrawn, unhappy little boy he was in year 2, I have no regrets at all about switching him into the independent system. I actually believe the pattern of early "failure" would have become a habit for him, and he would not be anywhere near where he is now in achievement.
Middle child is a high-achieving studious type, and could have gone and succeeded anywhere, but it seemed churlish not to give her the same opportunities as her brother in terms of extra curricular opportunities, drama etc... Also, frankly, I couldn't be bothered with handling the different holiday dates that sending her to the local school would have entailed.
Last child, also extremely bright, was actually showing signs of clinical depression after three years in the state system. Am not in the slightest bit sorry we switched her to a school (the laid-back prep also attended by her brother and sister) where she was able to be herself and heal from those three years. She is now flourishing at a highly academically selective girls' secondary school.