a school teacher is more likely to come from a wealthier, more conservative background

I couldn’t find stats for Australia, but in America teachers are statistically more likely to be Democrats than Republicans, so I don’t think this is supported.

It is also worth noting that, though I couldn’t find anything on Australian educators’ political leanings, teachers are one of the most highly unionised workforces in the country, and our centrist party (the one the media and many in the general public would call “centre-left”, like your Democrats) has explicit ties to the union movement.

a school teacher is paid poverty wages

In Australia they’re paid quite well. It doesn’t scale as highly for the average teacher as it does in many other highly educated jobs, but the base salary is pretty good. There’s the important caveat that teachers are largely expected to spend their own money on classroom supplies, though.

teachers are hired by administrators who are usually men, men who can have unaudited privilege

Teachers in Australia are hired by the department based largely on very impersonal factors like qualifications. There’s not a huge amount of room, at the level of classroom teachers, for that kind of bias to have as much of an effect. What more personal decisionmaking does happen is done largely by principals, who are former teachers themselves. Because hiring is done at the department level, principles can get involved in decisions like who gets a job at which school, but the fact that they have a job at all is much more impersonal. The promotion and hiring of principles and other non-classroom positions may be a different question.

That said, I’m not disagreeing with your main point. It is a systemic failure. At a scale far larger than merely within schools.