With respect, most of that refers to the private health subsidy that was introduced by the right wing governments to cover their asses after cutting funding to the public system. (waiting lists increased, "performance indicators" suddenly went down, etc)

This is the part that has now become expensive for the Aussie Govt to maintain and is bleeding the available money for the public system dry. They are looking at cutting it down at the moment.

Private health cannot work if you have to pay shareholders dividends. The Govt can run a system more effectively because they can negotiate bigger deals (lower costs overall) and the Govt does not have to PAY share holders (in fact "shareholders" pay them by way of taxes).