I can’t say I’ve ever seen uniforms do anything to combat the class divide. Better of kids had clean, well fitting uniforms and poorer kids had ill fitting hand-me-downs full of holes. Then there is bags, pencil cases, football boots and all the other bits and bobs that go along with school. If anything it’s a just a myth that certain people keep telling themselves to pretend the class divide doesn’t matter in education.
I think it’s to prepare them for wearing a uniform at work more than anything.
As you say it doesn’t really help the class divide at all.