I wore a uniform for 8 years in Catholic school.
We had navy shorts until Nov.1 and after April 1....all year round we wore pleated plaid skirts,and either a v neck sweater or a white polo. All had to come from the uniform store, which made it so easy to get dressed every day. I loved it. My only complaint was when it was literally 40 below in winter, and we had to wear skirts and BARE legs....any tights or anything and it was detention time.
As far as hiding who could afford nicer clothes, you forget that kids still wear Nikes to school on gym day and carry North Face backpacks....it was nice for the money issue to not be so obvious but trust me, its something that always sneaks in....