Yes, the dinner ladies are paid a wage.
However, there is only so much money in the pot! Certainly, the kitchen staff need to be paid for out of school dinner money as they wouldn't be there if it wasn't for children having school dinners. Outside contractors usually do the dinners and charge a set price for food and catering staff, presumably they make this the same for the nursery children.
Lunchtime supervisors- the ones who watch the children eat and on the playground- are paid out of school funds and I think funding depends on the number of children on roll. Nursery children won't count for the purposes of funding, only full time pupils, which explains why the parents need to pay some towards lunchtime supervision.
The nursery is also usually a separate building/unit, and the children not allowed to mix with the school children, which means you need more staff to go round. As an extreme example, if there was one child staying for lunch you would need 1 member of staff to supervise (though 2 would be preferable in case of emergency/protection from allegations on both sides). If that 1 child was on the playground with all the other children, you wouldn't need any more staff as the ratio would probably still be met.
As for not remembering stuff when you were younger, for a start you weren't entitled to as many as 15 hours free. And it wasn't as flexible as today. If I remember correctly, it used to be 12.5 hours per week, and school nurseries offered you a morning or afternoon place.