We have always had top-table private with the teachers federation. It is one of the cheaper options, and does pay reasonably well. We use private for most things that my wife or kids have needed doing. We do not have extras. We had it many years ago, but when we looked at it, it just didn't add up. Even with the three kids having braces, we are still ahead.
One reason we have for keeping the private health insurance is a family story. A relative had a growth that was benign, but easily operable, but because she was public, and without any means of paying herself, she went onto the wait list. She ended up waiting 15 months for the removal, and the growth had become as large as a football, which meant a much larger operation to remove it. She only really had the operation when the doctors started getting concerned that it was growing quickly, and may have been turning from benign to malignant. For us, the ability to just get things sorted quickly without too much financial concern is worth it.
We pay $340 per month before any tax rebates.