If the wife has status in Australia based on her Australian citizenship, which is most likely, exiting Australia with a Thai passport would flag her as being in violation. So it makes sense to get the tix and exit Australia with an Australian passport/name.
If DTAC is not required for Thai citizens, then she doesn't need to do it. She's entering Thailand as a Thai citizen, and her Australian status, citizenship, and name are irrelevant.
At times, Thai immigration will ask to see the foreign passport. E.g. when existing Thailand with a Thai passport without a foreign visa. I believe the intent is to verify that the traveler can actually enter the destination country and, in my experience, this has never caused any issues.