In CEHD we've been trying to figure out how to set up a responsive design that works for our sites for several years. The problem was quite simply that we couldn't figure out where to put everything... our academic departments have a lot of content, and some of it can be a bit wordy. The content needs to be trimmed down, but a "chicken or the egg" problem comes up. People have trouble understanding the problems with too much content until they can see it.
Off canvas allowed us to start a transition to more slimmed down and focused content. Everything can still be fully accessible, but not necessarily on screen all at once, on a mobile device. It also allows people to start really interacting with the content in a mobile arena...