Most of the prestigious private universities in US were established long time ago and they are not owned by individuals or families but by trusts who operate them on non-profit basis. I don't know about other Asian countries, in India, most of the private universities are owned by individuals with the sole aim of making profit. Education of students is secondary or most of the times not even a consideration. The students are asked to pay huge tuition fees and the teachers are paid next to nothing. How can such a college have any prestige attached to it?
However bad the standards may be in government institutions, at least, the goal is to provide education to the students.