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Maybe because many of the legacy students were born with a silver spoon in their mouth?

It's not a level playing field when it comes to the resources required to complete your studies. One student may have to commute for <2h per day to accommodation the can afford. The other can have a studio next to the campus and a car, both leased through their dada's company. One has to work part-time to bring food to the table. The other has extra time for sports and study.

Then they should have no problem getting it without those legacy admission privileges, so why are those in place?

This could also be simply due to the Ivy league institution providing the service being bought. In other words, the parents of Timmy might be fed up and stop being sponsors if he gets bad grades.

Of course in rigorous fields of study this is hard to do but if your rich kid is studying art, the grades are almost entirely arbitrary.

No - I mean this is also true for proctored high school exams like the SAT and AP scores. But also - no professor is changing grades based on who your parents are unless they are uber uber uber famous.