"Brumbies are not a good analogy...Brumbies...can be rounded up, shot from helicopters etc. but that would be/is politically 'difficult.'"
Your second point is exactly the analogy I was drawing, that cats could be a politically difficult situation when it comes to eradication, I wasn't drawing an ecological analogy between a horses and cats.
Main problem I suspect for the poor Phascogale/Tuan is the destruction/decline of its habitat, much of which is outside the 'conservation estate'. Brumbies are not a good analogy - as it would not be difficult to eradicate them - can be rounded
up, shot from helicopters etc. but that would be/is politically 'difficult'. Feral cats are the exact opposite in a large landscape. Always remember money spent on one thing in conservation means something else is neglected, given the limited pot of funds.
Meanwhile large scale land clearing, 'water stealing', coal mines, insensitive development etc. goes on unabated in places. Go for a drive, say into the interior and see how flogged it is, its a sad sight for a first world nation with so few people in it.
If you want a bird as a mascot for feral cat control then maybe its the Night parrot - that said, now we know how to find them, we are still in the early stages of working out their distribution and habitats, which probably is extensive. Got no idea
if their numbers are declining or not now. Got no idea if cats are a significant threat, though they could be.
That is not much use for common suburban birds, most of which do OK, cats or not, providing we provide habitat. There are better priorities for the conservation dollar.