"It cements a divide that the children have been aware of for years."
Yes. This is so true. This is exactly what the role I mentioned earlier, which half the class were given and the other half excluded from, did. It also gave the chosen ones opportunities to lord it over the others, in ways I won't describe here because they're too specific.
MaisyPops, I think that's a bit of an extreme interpretation. No one but you has used the word idiot here. I did think the response to you saying you reward hard-working children was unfair, but the phenomenon of teachers favouring children who bully others is real so, as a pp said, that's some people's reality. Teachers might, or might not, realise how the children they are favouring are treating others. If they don't, this doesn't mean the teachers are idiots. Children like this can be good actors, and very careful about not being nasty in front of adults.
In the case of my children's school, I believe most teachers did know what they were like. I believe the way they were treated was down to a combination of teachers with outgoing, competitive personalities admiring these children's personalities (we all like people who are similar to ourselves, don't we) and therefore overlooking their nastiness, and the belief that they needed their self-esteem raising/an outlet for their need for control (when really they needed to be taught some empathy). What annoys me about the second reason is that (a) it's all about their perceived needs, not those of the other children, who aren't doing anything wrong, and (b) it doesn't work.
I also think it's not always realised how difficult it is for quieter children to volunteer/tell the teacher they want to do things. As well as having had their confidence eroded over the years, so they probably doubt their own abilities, if there's a bullying culture in the class, publicly volunteering runs the risk of being taunted ("Oh my God, X thinks she can act!") and of having their nose rubbed in it when their request is ignored. After several experiences of not being listened to, and chosen, it can be safer to pretend you don't want things.
It's good to hear that some schools hold proper auditions for roles, though, rather than the teacher just choosing.