I attended a top-rate public school (Rutgers) on government loans, scholarships, and part-time jobs. There’s no way an elite private school could ever have been in that picture.
I received a great education. I think the main reason for attending elite schools such as Harvard or Princeton is to make contacts which, supposedly, will stand you in good stead later in your career. Maybe so. I made all my contacts after I entered the workforce, and I haven’t done too badly.
Given the obscene tuition rates and debt burdens today, I’d suggest you ask yourself about your kids: Are nebulous and temporary contacts worth a substantial six-figure investment? If so, you don’t want a “black book,” you want a platinum one.