If schools went back to a basic uniform of say black skirt and trousers. White shirt. And a generic black jumper or blazer how would anyone know that little tarquin went to the nice posh grammar school as opposed to the shit hole academy down the road.
Recognising schools by uniform is actually helpful, and improves safety in some cases.
I volunteer at an event with multiple schools — you'd tell if a child was separated from their school much faster if they were one blue jumper in amongst the red. Much easier for everybody to see where they should be too.
It also means if children are particularly helpful or well behaved, you can comment to their teacher if you didn't find out their names. And the converse is true — if they're messing around you can get one of their teachers easily, because they might not tell you which school they go to...
My school always said that when you're in uniform you're representing the school and it wasn't that uncommon to get members of the public contacting them about us when we were out and about. It might have just been to get us to behave of course. 