There are valid exceptions.
There are students who live in isolated rural towns that can’t easily access secondary school in particular, who need assistance attending a boarding school or the like and all of these are private. The government offers this assistance as Isolated Childrens Allowance, which is delivered in two parts, a direct payment each term to parents and there’s also a boarding component paid to the school, if the kid is attending a boarding school.
This includes those who live on grazing properties and farms. Quite often primary school is done by distance ed with a tutor employed on the station to help with classes. It exists for secondary as well but there are social costs; most opt to send kids to boarding school if they can.
To offer a true public option around that where these could attend a public school, more regional public schools with boarding capability might be required, perhaps in larger towns which already have public schools.
So yeah in the bush it’s not cut and dried.