I think the logic is that paid child care should be cheaper than the amount a full-time parent can earn. However, carers have to go through all sorts of training, police checks, insurance etc so that it isn't that cheap at all. Mind you, don't assume that it's so much of a gender issue these days. My friend's wife works full time because she earns more than him. He works part time to keep child care costs down and to spend more time with the children. Obviously, as they get older it becomes easier.
Another problem is diffusion of populations. In the olden days, granny would have carried out child care responsibilities while mum worked. If Granny is now also working or lives 300 miles away, things aren't so simple.
Interestingly recent surveys have shown that young children are happiest when spending time with their parents. Forget earning enough money for that Playstation. Take them for a cheap picnic!