It would be stupidly unpopular, but I actually think there should be some legislated amount the RBA then could regulate how much taxes go up and down. (Including income and/or corporate taxes)
Starting with the top tax brackets, and in extreme cases going further down tax brackets.
How this would work in practice, since tax is calculated annually, I dunno.
Bur it's patently insane we expect the RBA to control inflation and unemployment with so few tools.
Interest rate and quantitative easing/tightening, that's pretty much it, right?