I know several kids who were shut out of all their reaches. Valedictorians with cool EC achievements, kids with perfect test scores, etc. I didn’t read their apps, but for whatever reason, they didn’t jump out of the pile for any adcom. So yes, it happens. JhU and Cornell are slightly easier. You can’t get in if you don’t apply. And if you’re not accepted, you’re no less smart than if you were.