It doesn’t take into account the fact that private school pupils get years of advantageous education leading to better results
Where to start with that one!
Do you really expect Oxford, or any other university for that matter, to be solely responsible for redressing the imbalance in social equality that exists in the UK? Play a part by all means (contextual offers, widening access visits etc), but totally alleviate it, hell no.
Besides which you fail to acknowledge that most state schools educate the entire ability range, whereas most private schools educate a much narrower, and higher, ability range.
State provision caters to all - BTECs and Law A Level - neither of which are going to help Oxbridge entrance.
Billy who got 5 x grade 5 GCSEs will be much better served doing a BTEC Health and Social Care than Maths, Physics and Chemistry A Levels. Bucketloads of Billies in the state sector, very very few in private.
Social Inequality needs addressing years and years and years before sixth form.