Squatting high is easier, but easier doesn't work. You actually know this already, even if you keep the secret buried down below your brain stem. Easier has never worked, and you figured this out in about the fifth grade, provided you weren't in some remedial program mandated by your state.
When you memorized all your multiplication tables, arithmetic was a lot easier, wasn't it? When you diagrammed all your sentences, the next semester's writing assignments were easier, right? When you actually did all your homework, the test was easier. That type of easier does work.
Squats below parallel are your homework. The result of doing them is that you get stronger on all the other exercises, even the pressing movements, because squats make your whole body stronger - if you do them correctly. I know it's harder that way, and one of the ways you know it's wrong to do them high is that everybody else does them high. When was the last time that thing everybody else was doing turned out to be the right thing to do?
Deep squats done with a weight that's a little heavier each time you train affect your body in a way that no other exercise can. And believe me when I say that "other methods" have been tried. They just don't work. And it's not that they don't work as well, they don't work at all.
From When It Comes To Squats, Easier Doesn't Work by Mark Rippetoe