Why rich people prefer elite schools when most others doesn’t see any wort in it?

I take your point about “intellectually gifted” vs. “academically accomplished”, @observer12 , but let’s compare like-for-like between the freshman classes of Dartmouth and Michigan (based on the CDS of both). What’s evident is that Dartmouth has higher (sometimes substantially) percentages in the top brackets, and Michigan’s bottom end is below Dartmouth’s. Although the absolute numbers of kids in all nonzero brackets will be greater at Michigan because Michigan is over 5x Dartmouth’s size, walking around Dartmouth’s campus you’re statistically more likely to bump into a brainiac, and if you walk around Michigan long enough you’ll bump into kids whose scores would have kept them out of Dartmouth. I’d suggest that the differing concentration of brainiacs accounts for a lot of variance in the popular perception of both schools.

Michigan:

           SAT EBRW      SAT Math

700-800 54.5% 66.4%
600-699 39.7% 24.7%
500-599 5.5% 8.6%
400-499 0.2% 0.4%
300-399 0.0% 0.0%
200-299 0.0% 0.0%
Totals 100% 100%

             ACT Comp.   ACT English   ACT Math

30-36 80.4% 83.0% 64.8%
24-29 17.0% 13.9% 31.6%
18-23 2.5% 2.8% 3.4%
12-17 0.1% 0.2% 0.3%
6-11 0.0% 0.0% 0.0%
Below 6 0.0% 0.0% 0.0%
Totals 100% 100% 100%

Dartmouth:

           SAT EBRW      SAT Math

700-800 77% 83%
600-699 21% 15%
500-599 2% 2%
400-499 0% 0%
300-399 0% 0%
200-299 0% 0%
Totals 100% 100%

             ACT Comp.   ACT English    ACT Math

30-36 83% 88% 73%
24-29 16% 11% 24%
18-23 1% 1% 3%
12-17 0% 0% 0%
6-11 0% 0% 0%
Below 6 0% 0% 0%
Totals 100% 100% 100%

http://obp.umich.edu/wp-content/uploads/pubdata/cds/cds_2018-2019_umaa.pdf
https://www.dartmouth.edu/~oir/pdfs/cds_2018-2019.pdf