Hi Scuba Client,
I have the following comments re your first sentence.
Hyperbaric oxygen therapy is only publically funded in Australia for "eligible persons" who choose to be treated as public patients in a Public Hospital. Eligible persons include particular groups of Australian residents, and visitors from NZ and a number of European countries. If you are not an "eligible person" and wish to be treated as a public patient in a Public Hospital, you will need to be insured. For example, I recently dived with a diver who is an American citizen working in Australia - he advised that his purchase of insurance included hyperbaric oxygen therapy services.
I discovered the above about ten years ago when I did a technical diving course. One of the course pre-requisites was the purchase of insurance cover for hyperbaric treatment which was going to cost about 500AUD. I researched up the matter online and was able to argue to have the pre-requisite waived in my case.
Also, you will need insurance for ambulance services (both road and air-based transport) because these are not free for most "eligible persons", and which I have personally found to be expensive.
For your information, I was a subscriber to the local DAN organisation from 1994 to 2014 and decided to cease the subscription for the following reason. The basic insurance provided with the DAN subscription did not cover diving activity within 80 kilometres (i.e. 50 miles) which makes up most of my diving activity. The cover for the diving activity within 80 kilometres would need to be an extra purchase. In effect, I would be paying extra for services that I am already entitled to as a Australian citizen.