the idea from middle class professional in some schools that working class kids need to be educated in some form of boot camp.
I don't think anyone believes they "need" to be educated in a system with very strict discipline.
I think that the belief is actually that, because their intake don't come from advantaged homes, they are already behind their middle-class peers. So the idea is to make really effective use of every minute at school, in order to be able to catch up with - and maybe even overtake - their more advantaged peers.
So the strict discipline is there primarily to ensure no valuable learning time is wasted. The children buy in to it, in part, because that's how it's presented to them.
And since Ofsted reports that around 20% of school time is wasted on low level disruption, I think these schools have a point. Middle class, advantaged kids can afford to waste that time; disadvantaged children can't.