And why don't they all operate on the same admissions systems?
When you believe in and indeed embrace the state system (rather than private) it is quite a shock to discover that there is no single system, it isn't straightforward, and you will be exposed to a whole weird world of cheating/jostling/playing the system amongst your primary school parent chums to get their dc into the school with the best results. Even if the results simply reflect the fact that there is a selected element within the intake!
It sucks, doesn't it?