I think Australia has nationalized health care, and in such cases, he who pays the piper calls the tune.
Which is a major reason not to have nationalized health care.
Australia has a nationalised health care system, yes.
It also have a private health care system running alongside it.
Australians are free to choose whether they access and pay for the private system (or have insurance to pay for it), or whether they access the free system.
A lot of Australians (myself included) choose to do both at different times - if I need something fairly simple like a flu shot, or a medical certificate for work, I’ll use the government system. If I want anything at all complicated, I carry enough insurance to make sure I can go private.
If people are in a situation where they only have access to the government system, it’s because of the choices they’ve made.