The main context in which I have seen young people (sometimes quite younger than 10) caving as part of a caving club's activities, is where parents have taken their own and often friends' children caving.
Years ago I met up with Simon Edwards, a climber aged 16, at SWCC - a friend of Rob Parker's - who I went caving and climbing with in Daren Cilau in 1982. However, this was relatively unusual in those years since many young people caving then were university or college undergraduates, aged 18 or over. Back in the 1940s Agen Allwedd was pushed and explored for the first time by children aged 14 & 15, accompanied by one teacher - who often kept a watch at the cave entrance.
My first trip underground that I remember was aged around 4, at my own insistence, into a chalk tunnel near Rottindean in Sussex. I still remember how surprised I was that the tunnel didn't have a 'proper' floor - being unevenly cut and very slippery.
Martyn Farr told me that he went caving with his father in Eglwys Faen aged 10 and then the following year into Agen Allwedd, aged 11. He went to Turkey Pool and Coal Cellar in the same cave aged 12.
It is not to say that everyone has the same confidence and ability to be able to undertake such endeavours so young, but one thing is certain is that if you preach that such activities are frowned upon, then you're acting in a way to hinder people who would otherwise be quite capable of caving at a young age from fulfilling their potential in a legitimate fashion.
It is so easy to steer a discussion like this off into areas of 'political correctness', but the good work being done by youth & scout leaders and teachers, to give youngsters the same opportunities that we enjoyed as children, is to be applauded not admonished.