Contextualisation - it's impossible to come up with a perfect system.
One aspect that doesn't seem to be examined (or at least I don't think it is), is the cultural capital e.g. how many generations before have been to uni / are middle class?
Imagine a Cambridge-educated parent coming from a family where everyone - and several generations - have been to uni and good ones at that. This person perhaps then went into teaching (where salaries sadly are lower) and so perhaps lives in one of those aforementioned 'contextual' postcode areas, their kid attending state school (poor to mid performing) but who is likely with all that familial positive context (several generations going to uni, a sense that it is possible to go to uni even if at a poorly performing school) - and with a teacher in the family - is likely to be excelling. Likely to get a contextualised offer.
Compare that to a family where both parents come from working class, no uni education but who have 'worked themselves up' to earn good money and decided to send their child to private school. Their kid is likely to have a lot less 'advantage' educationally compared with the example above.
However, as the system doesn't consider context to such granularity, it is of course absolutely right that a state educated child (with some caveats) with the same grades as one from private school, should be prioritised. Research has shown - as mentioned above - that state school educated students go on to do better so there is some empirical evidence in all of this.