I tend to think the opposite. When I see school kids on TV (mostly in the USA) with no uniform, I think it looks terrible and scruffy. The vast majority of English schools obviously share this view. The other advantage is that you can wear school trousers and blazer multiple times to school without washing them, whereas I doubt any kid in jeans and t-shirt would wear the same jeans and t-shirt in every day. At 6th form it was wear what you want, and I genuinely found it stressful choosing (what was clean) from my wardrobe so that I was wearing something different, otherwsie if you wore what you did yesterday then people would comment.
The other aspect is identity. If the kids are doing something nice or naughty outside of school (i.e. on the way/way back) they can be identified by their uniform. I find this whole idea about freedom of choice quite baffling. Out of all the things they are forced to do at school like homework, classwork, PE etc, surely wearing correct uniform is the easy bit. It was quite telling at my school; all the ones who were good students and now have good jobs, didn't utter a word about uniform. It was only the naughty kids who were constantly being pulled up for it. Maybe there's a correlation!