I lived in Melbourne, AU for a while, and their system seemed good. The third-party insurance wasn't mandatory (like here in the EU), only recommended. But you could buy insurance (something like reverse third party insurance) where if someone crashed into you, the insurance would pay you for the damages and then they'd get the money from the other person. It was very cheap.
Note, however, that a form of third-party insurance is included in the vehicle registration fees: https://www.vicroads.vic.gov.au/registration/registration-fe.... For a regular car, the TAC charge and its 10% insurance duty are somewhat more than the registration fee (my most recent annual renewal had a $302.40 registration fee and a $413.60 TAC charge + insurance duty, as one garaged in a low-risk zone; that increases to $532.40 if you’re in a high-risk zone, which looks to be not far off “metropolitan Melbourne”).
The TAC charge being a form of third-party insurance and mandatory commonly misleads people into thinking that what’s normally called “third-party insurance” is mandatory, but as you say, it’s not.
You are just insuring your own property and for any damages the insurer will just go after the party at fault if it isn’t you (or “you” as defined in their policy wording). Pretty simple way to keep rates down the r profits up for insurers.
