morethanpotatoprints education is also the responsibility of the parent under law, otherwise what you are doing would be illegal. 
But why should one thing be a collective responsibility and another an individual responsibility? serious question.
Surely we either say we have individual responsibility to the collective good or we have individual responsibility to ourselves and no other. If childcare should be paid out of wages and not taxes, should education, health, roads, libraries etc,..?
Right now the average worker has been shafted for 30 years. All the wages we should have been receiving have accumulated in our bosses back pockets. Our bosses are crooked weasels who don't believe in the collective good, they neither want to pay out of their own money or pay through taxation, claiming "what me, I don't use those free childcare places, NHS hospitals, state schools, wouldn't touch it with a barge pole" maybe because they don't have to unlike the rest of us!
Either we should campaign for higher wages, so high in fact that we can all afford to pay our own way without state support, incl paying for all and any childcare or we should demand a modest but fair percentage of the wealth WE create, demand a fair progressive tax system that picks the pockets of the weasels and provides a decent education, childcare, health and welfare for everyone.