Awesome letter! I completely agree that midwifery lead care is the ultimate method for low risk women, (and even some "high risk" women), especially if it's continuity based.
I went private with my first child, for the same reasons as you really. And it was a huge mistake in hindsight. You can't have much more intervention than a CS under a general, all of which could have been completely unnecessary. And it affected my birth choices greatly second time around.

For my second preg I started out going through the public system as I wanted a the best chance of a VBAC. Unfortunatley though, there were no Continuity of care options in the public system for me as I was seen as "high Risk". I did not enjoy seeing a different midwife/ob/registrar at each visit and was told different things each time. I really wanted to build a rapport with my care provider. It was so so imporetant to me that I had a known person caring for me who knew my story and my wishes IYKWIM. So I ended up seeing the senior public hospital Ob at his private practice ( I had heard that he was very hands off and also very pro birth centre) and clicked with him instantly. And although my second birth ended up being a CS (my choice in the end) in a private hosital. It was positive and wonderful and I don't think I would have had as much control if it were in the public system because I wouldn't have had a "known" care provider.

So I guess for me, first preg, going private was a huuuge mistake, but it was a wonderful experience second time around.