Interest in getting young Johnnie into a specific university doesn't account for the fact that we are talking about billions of dollars in endowments. Most small donors know that their $100 per year won't cut it when it's time for their offspring to apply for university, but they send that cheque anyway and it all adds up. Three of my DCs so far have managed to go through university almost debt free thanks to need blind admissions, made possible by donations and stewardship of the endowments.
American universities have massive endowments because they are not shy of asking for money. I get begging letters at least twice a year and phone calls during phone bank season from all three of the universities, two private and one public, from which my DCs have graduated. My DCs get the same, and the phones are manned by students doing a very hard sell.
My own Irish alma mater tracked me down a few years ago with the donation basket outstretched. In Ireland admissions are done by the Central Admissions Office - your exam grades go into the computer along with your indexed list of ten degree courses, and out comes your allocated course, with your destination determined not just by your results but by the results of everyone else applying for a place on your preferred courses. It's anonymous, completely impersonal, fair at point of entry, a little like a rock tumbler. The appeal when it comes to donations is that you will be participating in sponsoring a student who might not otherwise be able to attend. There is no hope whatsoever of an adjustment to the algorithms of the CAO in your child's favour. Big business donors have given a lot of money to build facilities for various different faculties. Quite honestly, I wouldn't begrudge a donor's children if that donor supplied a library.
American private elementary and high schools do a massive amount of fundraising too because they do not receive any federal or state funding. The vast majority of the work of fundraising for private schools is done incredibly professionally by parent volunteers.