I really still do not get this argument.
I'd like everyone who is against the suggested after school clubs to sign on paper that they provide their DCs with an enriching environment at home, incl. their own playground in the garden, tons of books and loads of other children to play with. If it turns out they don't, then I am allowed to sue them - and be a millionaire by tomorrow.
I know a lot of mums in RL who proclaim to be heavenly mums online. But really, all they do is pick up kid from school and let them watch TV or play PS at home. No taking them to music lessons, etc.
Parents are often guilty of transferring their own desires on their children, e.g. "I have the money, but I don't think my kid will fit into private school" often actually means "I have the money, but I don't think I'd fit in with the other mums". I think this is one such case - most people against the afternoon clubs seem to never have tried it out. They just "know" their kids won't like it.
My mum used to think I'd hate going to summer camp (as in weeks away), but she was equally upset when she figured out I did not want to go home! You might realise that your kid would not want you to pick them up when they are playing with their friends at school...