An app would definitely make AO3 easier to access for a lot of people - but how would that app be developed and maintained by an entirely volunteer workforce? Not to mention that it wouldn't be one app, it would be at least two. One for Android and one for iPhone. And then you bring the app stores into it and the apps would be taken down in fairly short order because of the content that AO3 allows.

I don't personally see a way to make an AO3 app a viable option without a public API, and they can't release that until the Archive is at least at a 1.0 release and out of beta.