CASA doesn’t use the AAT.
People affected by CASA’s decisions use the AAT.
The AAT has jurisdiction to review a very broad range of administrative decisions at the Commonwealth level. That’s Commonwealth policy. (And, to continue on a theme, if you don’t like it, it’s pointless arguing with CASA about it.) But you could give it go: lobby the Commonwealth AG to remove the AAT's jurisdiction to review CASA's decisions. CASA would love you for it, I suspect ....
The AAT gives the person affected by a decision the opportunity to have it reviewed, on the merits, by someone external to the agency which made the decision. Take that away, and all you have left is judicial review, which is very narrow, very expensive and has nothing to do with juries of peers or beyond reasonable doubt or any of the other folklore that persists.
By the way, numerous people on the AAT are Federal Court judges.
Here’s the fundamental aspect of AAT review that jars with the kinds of people that gnash and wail about CASA on this forum: If you seek review of a CASA decision, you will almost invariably have to give evidence if you want the AAT to understand aspects of the matter about which you alone know, or have first-hand knowledge. And if you’re a bush lawyer or smart*arse who thinks the AAT won’t see through your half-truths, selective-memory, or god’s-gift-to-aviation attitude, you are - not to put too fine a legal point on it - stuffed.