Yes it is cheaper if it's other people's taxes. That's why no-one campaigns for tax cuts so they can afford childcare.

To make it more explicit, subsidized child care is cheaper for parents, because everybody pays taxes, but only parents receive the subsidies.

A society without children is called dead the next generation. Not that I'm pro-subsidies (never used any) but I can see why there would be some collective advantage about the previous generation having had children (that's why you're here...) and we extend that to the next. This also benefits those without children because they end up getting a pension from other people's working children. (your pension typically isn't money that you put in the bank, contrary to what most people seem to think).