good private school provide better quality of education in all espects which may bnenfit a kid in his/her life time, regardless aiming at ivy or not.
remember, education is special type of investment whose return can not be just valued or measured by how much money a kid will eventually make or which college he/she goes in.
a well-educatd person may not be wealthy, or doing very ordinary job. but hopeflly, they feel good about themself, they are more confident, have high selfsteam and integrety.
