Holy s**t!!!! I was about to write a post lecturing you about limiting yourself to T20s, but I went back and saw from your WAMC post that you did everything right. What do you think happened????????????
If this happened to you it could happen to anyone. When you talk about applying earlier, just how late did you apply? Given your stats, you should have received a look no matter when you applied, as long as it was before the deadline!
There are no obvious weaknesses in what you stated above, so there almost has to be a bomb somewhere in your app (essays, LORs, etc.). 16 schools is a little on the light side, but the schools you were talking about seem fine. Crazy as it might sound, I wonder if there is a chance that your list wasn't heavy enough, and that you found yourself yield protected out at most of your schools, without enough shots at the higher ranked schools to give yourself a reasonable chance to be successful this cycle?
I'd love to hear other opinions, but it kind of has to be one of these two (terrible essays and/or LORs, or terrible school list). It's not your interview skills, because you didn't get that far. Given the profiles of everyone else reporting success this cycle, it sure isn't your stats or ECs, which are the two most important metrics. I feel terrible for you, and hope people who know what they are talking about weigh in here.