It has smaller persistently arid regions than people think, and the corollary is that there are huge intermittently arid regions which spring into visble productive green life.
It also has a giant water system which runs almost the length of the eastern side, far inland from Queensland Channel country to the mouth of the Murray in South Australia, with many tributary rivers feeding in and being fed. It has a giant aquifer.
The thing is that we're looking a 50,000 years of fire driven deforestation and arguing to restore some belief in past verdency ignores what might be the lived reality of these landscapes which are feast and famine and have been for thousands of years.
Modern ag is much less kind, and has caused some massive destruction and topsoil loss and biodiversity loss. But, the goal in Australia wouldn't necessarily be a permanently verdent inland, it would be (I think) to work with what we've got.
Getting rid of millions of feral camels would break some people's hearts, judging by how they romanticise the feral brumbies in the victorian and nsw high country, despite the damage they're doing.
Getting rid of the dingo fence would be a good start: there's more growth outside it than inside.