I am working in a school with a mixed neighborhood and our students do not wear uniforms, as uniforms are uncommon in Germany.
For historical reasons, anything related to military is seen sceptically by many parts of our society.
The differences of the financial backround are very visible because of that and sometimes I would really like the idea to cover them and give the students a better feeling of community.
Though most students will see the financial differences of each others families anyway as school is a place where people get close together. Also it gives us as teachers the opportunity (and sometimes the duty) to discuss adequate clothing for a "professional" situation - with mixed results as far as I can see.

In the end I can not share your enthusiasm for school uniforms, but I would love to try it. Thank you for your great post.