If you're living in an area where public school quality is dubious and paying for private school would considerably improve your child's education, then no doubt it makes sense to do that.

But if the public school is pretty good, and your child is likely to pursue the kind of college education where going to an expensive university can pay off immensely in their career, then probably private school isn't the best investment of your money. Doesn't it make more sense then to save your cash and use it for their college later? Regardless of the legal limit of adulthood at 18? That is, assuming that you are willing to pay a fortune for your child's education, which as you point out is not necessarily a requirement of good parenting.