It has nothing to do with the length of grass.

Ideally, I'd like to mow the grass to 3". i can't do that because there's not enough lift to stand the grass up straight to get that cut. So I've lowered it and that gives a better cut. 

It won't pick up anything if it's on the lawn below blade height though. Leaves, a small piece of paper. Heaven forbid you drop some grass while emptying the catcher. Anything in that pile above blade height will be gone, but anything below that will remain no matter how many passes you make. There's just no lift, whatsoever.