Earlier quoted context omitted.
The healthcare isn't free no matter how many times you people say that. But you're also wrong about Australia being "a very similar society to the US". Maybe at one time, but Australia has some very authoritarian laws these days - from gun control to internet filters, etc..
Only in the distorted, leftist mindset are things free because they just happened to be paid with taxes.
For the poor, (i.e those that earn For those that earn > 28k, they pay tax, which a portion of goes to healthcare. So from 28k to probably (random guess) about 70-100k, healthcare is heavily subsidised. For 100k - 200k healthcare costs probably about as much as it would if they just paid for it themselves (given the wealthier tend to be healthier). The 200k+ they are probably paying more for it than they use.
But those who need it most (i.e the poor/poorer) get it free/subsidised.
This is called a progressive tax system. If your care about the majority of your society (keeping in mind, in australia the mean wage is around the 50k mark), then it is without a doubt a better (utilitarian) solution.