I think it's one of those things like healthcare, or social care of the elderly, that we should all pay for, in the hope that we won't need it, but in the expectation that we might, and if we do it will be covered.
I think that every able bodied adult should be taxed (or obliged to contribute in other ways) from the end of their education to the beginning of their pension, and in return have the use of things like libraries, roads, transport (which I would also subsidise) as well as education, health, access to social housing and a decent pension free at point of use. Childcare would be part of that package.
Fair enough, unfortunately not everyone would live to claim a pension, fortunately not everyone needs social care or a lot of expensive health treatment etc, but those who do should not have to worry about paying for it.
There could be solutions found for people who think there is no point in having children if they are in nursery or playgroups for a couple of years. They could volunteer in the evenings or something. The detail would need to be sorted out, but the principle seems to me fair. From each according to ability, and to each according to need. Access to the benefits of living in a first world country would not depend on income, as it would be entirely contributions based (however that worked out), but taxes would be based on income, so that those on higher income paid more.