It's true that the studies are merely correlations, but there is logic in drawing the conclusion that influences other than the student themselves can impact on academic achievement. Socio-economic status being significant in that.
If it was influential, then it would at the very very least showed up as a correlation in the ACER study - but it didn't - not even a simple correlation. SES could not explain the variation in student achievement for Asian students. There is no logic, and it is very much illogical, to imply from correlation that there must be causation. It is even more bizarre, to still hold on to the view of causation when a study has found that there was no correlation. If SES impacted on student achievement then it would have showed up in the ACER study, regardless of race.
an average student will logically have a better chance of success if they are among people who value education (usually these are people who have some form of affluence) and if they have good teachers.
If that was so logical, it's logic would have showed for itself. That claim you made is an empirical claim. The first one being the existence of peer effects and the second being the effect of quality of teaching on student achievement. Not to say that the claim is false, but peer effects are notoriously difficult to prove empirically because there are so many other biases that could be affecting what might appear to be peer effects. The major one is selection bias i.e. students who are smart might very well tend to hang around with other smart people, and that's why you find that kids who hang around with smart people tend to get higher results. But again, that is not the topic.
I just think that the spread of 'good' teachers should be fairly even across all public schools.
That's just not how it is at the moment. A good deal of why that isn't happening is a result of government imposed restrictions. The problem is that individual schools are not free to set their own compensation arrangements to meet their own individual needs. Schools that serve predominantly disadvantaged populations need to be free to offer higher salaries to the teachers to be able to attract teachers to work in such conditions. The current evidence shows that because the same salary schedule is imposed on all government schools that this creates severe problems for schools with particularly disadvantaged populations because they are not allowed to deviate from the uniform salary schedule and offer a higher rate of pay to teachers to compensate them for the tougher working environment. Government imposed uniform salary scales mean that teachers choose government schools based on non-wage factors. So we get the perverse effect that the most sought-after government school teachers are in the cushiest government schools.
the rich should not get priority to supposed 'free education'. (Through buying into richer areas that are in the zoning of better schools).
That is not the aim of government education and it should not be
I agree with that it's a real problem and it mocks the notion that government is providing a "free" education - this is even ignoring the whole "voluntary fees" debacle. Here is the most recent Australian study on it:
"Finding that a 5 percent increase in the median UAI (approximately one standard deviation) is associated with a 3.5 percent increase in house prices—or $13,000 at the median 2005 ACT house sale price...Since houses in better school zones are more expensive high-quality public education is not costless. The price of buying into a good school zone may prevent poor families from accessing the public schools of their choice. Given that education can transform the social and economic opportunities of the underprivileged, such social exclusion may perpetuate cycles of disadvantage if left unaddressed."
http://econrsss.anu.edu.au/~aleigh/pdf/SchoolQualityHousePrices.pdf