Unless it is an emergency you practically does not get good care unless you went private, even for private the wait time is too long. I am not impressed.
I went to a private hospital ER with an infection that was spreading five times over two weeks before being admitted. At that point I needed surgery.
Public isn't any better. My wife is allergic to codeine and had to stay awake all night after an injury that left her hospitalized. Why? Because doctors kept trying to give her medication that she's allergic to. The doctors and nurses made fun of her for being in pain and refusing medicine. It took a specialist coming in the next day and chewing them out to give her anything. They wouldn't even give her an extra ibuprofen.
Honestly American healthcare is very good. Expensive, but good. I am in a position where I would rather pay with cash upfront than risk to my long term health.
Australian GPs would be very far from able to practice in the US.