It certainly doesn’t matter like it use to. Large factor is certainly an exaggeration unless your family bought a large building. Go to alumni boards and you see how many feel this has dramatically changed, there are a lot. I would say small if any amount of influence.
With 35% internationals, first gen, URM, and all the other classes/groups that they are looking for, legacy has certainly taken a huge hit in the last 5 years. Expect this to stay this way till they realize they aren’t getting the donations they are use to. Even though their endowment is huge, donations were down over 10% this year.