Because a school is expensive does not necessarily mean it will be worth the expense to send your child there for an education. That will depend on the child and the school. Some schools are very expensive, and also offer a good education, but admit students more on the ability to pay than on academic achievement.
Other schools are expensive but admit students more on the basis of academic achievement than the ability to pay. These schools have large endowments -- Exeter over 1 billion, Choate over 1/3 billion, etc-- and offer very substantial needs based tuition assistance. These are the schools that are worthwhile, assuming your child can qualify. These same schools will also occasionally admit students that are less qualified if they are a legacy child or if their parents are very wealthy and might make a nice contribution to the endowment fund. But those are exceptions, not the rule.
The kinds of educational opportunities offered by the best of the boarding schools far exceeds what is available in public education, or run of the mill private schools.