Enigma, the problem with a fixed fine and penalty points is that they don't make the driver think about the potential consequences of their behaviour. It's just an annoyance and a bill to pay like any other motoring bill. Having to face a classroom full of kids and think about how their speeding could have caused one of those kids an injury or even worse death is far more potent. Every time they see a school they will have that mental image of a class full of kids in the back of their minds and all but the outright wreckless will ease of the gas that little bit more. I think it's a great idea.
Also, from the other side, you're also educating the kids. Maybe when they grow up and learn to drive they'll remember how humiliating it was for that adult to have to apologise to you and that could affect their driving too. The more contact the police have with kids while they're young and impressionable, the better their relationships will be when the kids are older. This sort of thing may help repair the respect people used to have for the police that is evidently lacking at the moment and it's two-way street arrangements like this that can make a big difference!