Hi James,
I've not looked at the Moodle Mobile app for quite a while. I remember when we were looking at the options already available (before starting Oppia), that at the time the Moodle mobile app had very limited offline capability - perhaps only able to download files from the course. But this was a few years back now, and I'm aware that there is more offline capability - but it's not available across all activity types and as you say the quiz is a big one from our point of view.
Also at the time, I found the user interface quite horrible - although to be fair it has massively improved recently. For the types of users we're working with having a very simple clean interface for me was a priority and given the flexibility Moodle has with the course structure, activity types etc, means there a bit of trade off between simple navigation and feature set.
I suspect that the Moodle development community will get to having many more activities available when offline - but it may be more to do with their user group priorities and their target learner audiences are likely to be much better connected with wifi/gprs.
Hope that helps,
Alex