We wouldn't go without it even though its costing us a fortune. I've made use of it plenty of times with private births & endo treatment alone. Here's a few examples... of course one of the top ones is not having to wait on waiting lists..
My baby was also in special care after she was delivered for 8 nights, she had the same paed treat her everyday & he was available for the nurses to discuss her case when he wasn't there. She also had a lumbar puncture at 3 days old and I felt much better knowing he was doing it with the experience he had. They also let me stay until she was discharged so I didn't have to go home without her. I had an emergency csection but I didn't pay for the spinal block and the paeds fees were all bulk billed.
I have pregnancy problems & saw my ob for the 1st time wed, we had a plan, he discussed my situation with another specialist and the very next day they booked me in for a complex surgery which i had the following day (yesterday) I will be out of pocket a fair amount but there is no way I would have had this quick treatment in public.
When I went to the local public hospital for suspected appendicitis I was admitted as a private patient, I was moved to a private room & could choose my own experienced surgeon over a surgeon in training. Fortunately I didn't need the surgery but I felt better knowing it was an option especially if my kids have any problems like this in the future.
Do be prepared though to be out of pocket for some costs, all obs charge differently so call around and see what you would be looking at.