I am the same as Divvy in how i feel about the importance of it (and I am also in melb but didnt grow up here) - and my mum was a single mum who put me through a private school with a lot of hard work and I now realise juggling!
I think it depends on the school... and the kids and the family and friends...
there are so many reasons for me choosing the school i did...
my boys will go from kinder just bc i love the school and the community and the philosophy... it may mean we miss out on some things as a family but this is really important to me. that said, i have a good income and so does dh so we can still do holidays etc too (i think, at the moment not but this is a tough time for us) - but when i think of the fees it does make me think harder about it.
I live opposite a great public school and i see the benefits of that too (all friends living 5 mins away, local community etc) - but this has been the right choice for us.
So for my famuily i would choose the school but there are lots of factors that come into that for each family.