GRE is NOT a selective measure but a REJECTIVE measure. This means that if you score less than lets say 315 for an IVY league college you have high chances of getting rejected in the preliminary rounds itself however if you score above 330 it does not leverage you in any form. It just means that you have lesser chances of getting rejected in the initial rounds of scrutiny. Now the Admission Process for US Universities is a Black Box and there are a lot of theories regarding it. Personally, this is the one which seems most trustworthy to me as it appeals to logic.
Numbers in the form of GRE Scores, TOEFL Scores, CGPA are your first filter. I am not saying all of them are but some/most of them. Why ? Simple, If you have millions of applications each year coming in , how do you short list them to thousands ? Do you open each SOP/LOR/Resume and evaluate them or do you put a number filter ? I personally think to short list from such a huge pool of applications a number filter (GRE/TOEFL/CGPA) is the first step. When you are to thousands you can afford to open up and glance through people’s.