Or, on the contrary, it might exacerbate the situation. Everyone looks the same, which means people with quirks will stand out even more. And again, it will be the same old story: "He's not like us, we don't want to interact with him." Besides, uniforms have the annoying habit of wearing out, getting stained, and tearing. So, as a result, the wealthy will often wear new and good-looking uniforms, while the less fortunate will wear patched and stained ones.
Children grow faster than uniforms wear out, I assure you. Unless they're wearing hand-me-downs from older siblings.