What if a school sought out students likely to become future government policy makers?

Hello-- Yale, Harvard, etc. Take a quickie glance at the vitae of the SCOTUS and the Cabinet members.

What would happen if the statistics of incoming freshman and graduates were used to solicit new customers?

Done-- seriously, already happening. College Board is allied with the top tier in promoting it. I'm not at all convinced that some of the posts at places like CC aren't deliberate con jobs intended to produce DEMAND in order to inflate the numbers of applicants so as to make a school seem more "prestigious" by virtue of the selectivity, which then lifts the institution in sort metrics at various database sites (like College Board).
What if they went all modern advertiser and used tricks like markup/markdown? (increase tuiton by 20%, then send out 20% discount coupons.)

Again-- already happening. IMO, anyway, this is precisely what second tier private schools are doing by offering "Presidential Award/Scholarship" that amounts to a 10% discount on tuition. Some of that $ is for merit and some is for financial need, but they aren't necessarily showing anyone the (proprietary) rubric for deciding who gets them either way. KWIM?

Or had the idea that giving someone money now signficantly increases the chance that person will give considerably more money later on?

What do you think drives "make students live on campus" nowadays? Some quants got together and told College Presidents what seems to correlate most strongly with "brand loyalty" and "alumni giving" rates, that's what. Seriously. I know someone in this industry, and that is EXACTLY what they do-- they find the numbers that lead to the greatest amounts of donations in the future.

What if a school competed and advertised based on reputation? Listed famous graduates, nobel prize winners, diversity statistics, winning sport teams, etc? What if testimonials from former customers helped attract new customers?

Again-- this IS happening. You know who Reed features in their catalog (which I happen to actually have a copy of)?

Steve Jobs, that's who.

Big 10, Pac-12, and SEC schools regularly feature their big-name bowl teams in such literature. They feature alums who are famous... alums who are rich-rich-rich, and alums who may not have even completed a degree before going on to fame and riches.

Schrödinger's cat walks into a bar. And doesn't.