I think it would depend on when you began the uniforms. If kids have never done anything but uniforms, I think your scenario could easily play out. However, if kids had worn what they wanted until 6th grade, and then the rule was implemented, I think there would be resentment of the rule and kids would try to rebel. Plus, people would still know who belongs to what “class” in school.
Pardon me — I don’t see the link to school uniforms. I wore a school uniform until college.