Genuine, naive question - schools' postcode lottery

[namechange0123]

I hope not to offend anyone with this, it's just something I have been wondering for a long time.

I come from mainland Europe, lived in England for 7 years now and loved it enough to get my citizenship, but this is something I can't really get my head around.

Our school system is completely independent on where families live - for primary, people register to their DCs absolutely everywhere, sometimes tenths of miles away if that means being closer to their workplace (which IMO makes enough sense). For secondary, choice is strongly dependent on the subject (more focused on humanities, sciences or technical/vocational), but again, where two similar schools exist, choice is completely free.

The results is that all schools are equally mixed, there are no schools with stellar results due to rich, heavy tutoring, over involved parents and no working class ghettos.

I'm genuinely (please, please trust my naivety) wondering why England insists on perpetuating this extremely classist system of good and bad areas with associated house prices, grammar system with expensive tutoring for the 11+ which not always then reflects true ability (but why also select on ability at such a young age? I know several people who were awful in school and thrived at uni!) , a system that ultimately kills social mobility.

There's surely something I'm missing as I really can't understand. Can someone explain?

@lljkk I am talking more of something like the current equivalent of £15/month.

But you're right in the sense that we are wrongly trying to compare two different societies and that model wouldn't be possible. I don't want to suggest this model is the absolute best, I'm just wondering if something can be changed here.

DH was born in a working class family, MIL was a SAHM and they had little money. He went to uni with bursaries and nobody asked him which secondary he came from. Did a PhD and moved to the UK where he is now a uni professor. This would have been far harder if he was born here. It's not fair, whatever model you may want to demolish one piece at a time.