And as for wasting time battling over a type of shoe - it is not us, but the teachers who make an issue of this.
I sent my child to school wearing incredibly good quality shoes which are around £50 (I got them in a sale, but still) and he wore them for about 6 months before one day, being asked to remove them and wear his plimsolls for the rest of the day.
He came out of school upset, I asked what was wrong. He had slipped over twice in the playground as his plimsolls are not outdoor shoes. He was distressed and embarrassed at being singled out like this.
I went to the teacher - she said 'they are trainers and they are not black'. I said 'we have another 6 months to wear navy shoes. You are not supposed to enforce the new uniform until then. And I would not send my childto school in trainers.' She still moaned, so I went to the HT who initially said the same thing, then backed down swiftly when I told her how much they had cost, how long he had been wearing them for, and that there was no way he would stop wearing them till they wore out.
she made a fuss that they had a small logo on them in a different colour (not trendy - just the name of the make in tiny letters) and said next time they must be completely plain. 
Anyway eventually they did look a bit scruffy, and so I got him some plain black ones from clarks (exactly the same style - anything with velcro could be called a trainer, his entire class wears the same thing) and within a week they had holes in the toes.
I could not find the receipt and as they were bought in the sale too, I let him wear these items till the end of term...no complaints, I presume because they were from clarks. They had massive holes in them and looked terrible.
It makes no sense.