Hiya, in addition to reading these great comments here, you may be interested in this thread: Public, Private or Birth Centre?
As others have said before me, it is such an individual choice.
As you kind of haven't been given a choice (what with the HI not covering you) then there's no need to agonise over the decision IMO
I wouldn't be concerned what others think of your decision to go public. This is just the first thing in a long line of decisions you will make in regard to your baby that others will have an opinion on Learn to be confident in your decisions and to hell with everyone else - this is your baby, you're the mum and it is always going to be your call.
FWIW, I have private health insurance and I still chose to go public, and had such a great experience that this time I have chosen to go public again. Haven't come across anyone who has criticised my choice, but perhaps I am lucky there.
All the very best for your birth!