Firstly, waiting timed as mentioned by a few pp's. Here's some examples. Througg the public sysyem, my appointment to see a neurologist was 13 months, to see an alleegist was 15 monthe and to have an emergency appointment with a bowel surgeon was 6 months. My friends dh melanima surgery was constantly delayed for 6 months. My husbands cancer surgery had a waiting list of 3 weeks to see the surgeon and a waiting list of 3-4 months for the surgery (this was for a very aggresdi e cancer as it turns out). We went private for this, saw the surgeon that day, biopsy organised for that afternoon, results the next day, surgery a week later. If he went through the public system, his cancer would have progressed from a grade 2a to a 3+ in that time, taking his survival chances frim 80-30%. So not a total waste of money at all and dh was previously fit and healthy and young, not using a singly day of sick leave for three years before cancer.
Secondly, I don't think its a good idea to use a private hospital if you don't have insurance. If your birth is straight forward, yes it can cost as little as 4-5000$, but if you have an emergency caeserian, baby is sick, needs the special care nursery, even with a transfer, you may find yourself needing to sell the house, car, whatever to pay these bills. Not a good idea at all.
Oh and just to let you all know. Ambulance cover through most phi, does not cover non emergency (like non emergency patient transport). If you want to take out ambulance cover, there is a three month waiting period on non emergency and pre- existing conditions (although this does not apply to some states).