It seems to me to be a form of extortion for private profit - especially for publicly-funded schools. I wonder if it's ever been challenged in a court of law ?
You're right. I went to a private catholic schools, in America, in the 90s. We had uniform requirements that were basically dress shirt, tie, dress pants and shoes, and we had to shave. I was always getting in trouble for not shaving. It wasn't business formal, but it wasn't business casual, either. Kinda business formal without the jacket. Keeping your zipper and buttons in a straight vertical line was not strictly required, but our director of student conduct would jokingly lecture us about that in the hallways, even though we would not get written up for it (I think that's called a bunt line? Maybe?) We did not have a specific supplier that we were forced to buy uniforms from.
I'm pretty sure the girls could buy skirts from whoever they wanted, but it had to be the right type of plaid, which I think limited their options. I'm pretty sure there was variety in the pleating on the skirts, so I think that probably meant there were multiple suppliers of the skirts. I don't think they were told that they had to purchase skirts from a specific company, though.
I think what happened is that public schools got defunded, so these uniform companies came in and offered schools kickbacks for requiring students to wear their gear, and only their gear. At best, it's a school tax that only parents have to pay. At worst, it's an abuse of power, and a scam to profiteer off of government power.
Uniforms are stupid, anyway. The studies saying they help students learn were all funded by uniform companies.