If you do have the chance to land a job that offers private medical insurance or Medicare Supplemental Insurance as part of the package then you would be well advised to grab it with both hands. Large firms get a good deal on the price of private medical insurance, whereas if you try to buy it off your own back it may work out too expensive.
There are definitely benefits to having private health insurance, even if you do qualify for free healthcare where you live. Apart from anything else, you have the peace of mind from knowing that you are covered for just about anything if you fall sick or suffer an injury.
You often also get treated much more quickly if you have private medical insurance as many hospitals will put you to the top of the waiting list. This may not seem fair to other people but it is the case and I have seen several examples of private patients getting quicker treatment than state ones.
Some insurers also offer a cash payment if you choose to go on a public rather than a private ward and this can be a real benefit if you are unable to work through sickness.
Free healthcare is a great system and yet many people do prefer to have private medical insurance if they have the chance.