[roenxi]

If we start with the assumption that the cost of childcare is costly enough that it would lead to an unacceptable drop in living standards for the average couple, and then force them to pay that cost anyway (regardless of whether they actually have children) it is unlikely that the follow up is going to be the couple having kids. They'll probably be busy desperately working to get their living standard up to a state that is bearable.

It isn't cheaper to raise kids. They're actually losing more under the socialised system because they still have to give up enough resources to raise the kids and now also to cover inefficiencies in the government program. On average everyone would be worse off. Or you're going to be taxing grandma so instead of her providing helpful childcare services she has to go and work at McDonalds to make up the difference or something. Society is geared towards supporting children already - routing the resources through the state or through the family can't make it easier. Men work to support families, women work to support families, grandparents have nothing better to do than support families. The resources were already tagged to support families. The government can't magic more resources into existence if raising kids is expensive. They'd be taxing families so instead of using the resources to support their families, the resources are being ... handed out to support families. There are no gains, so it isn't going to help.

State spending can reallocate; I can see some potential success in using childcare to free up high performing parents. But if the problem is median experience, reallocation can't do much.

Postscript The taxes in these countries are no joke. Young families are losing a lot more to the tax system than the "free" childcare makes up for. If you traded the free childcare for paid childcare and low taxes, they'd likely be in a much better position to have kids. [Taxes] approx. = [Cost of Services] + [Admin Costs] + [Cost of Rorts]. That isn't making it easier to fund a family.

[NineStarPoint]

Main problem with your logic is that it assumes a situation where most people are having kids. Given the situation in Scandinavia is that many people aren’t having children, you end up in a situation where everyone is being taxed to fund childcare, while most people aren’t actually taking advantage of that taxation, so those who are can actually gain more resources than they put in.

[roenxi]

The average woman in a Scandinavian country has 1.6 kids. That suggests it is quite common. Going by averages, literally every woman has a child, and half the men.

In actual practice there will be particularly fertile women that have more children and their childcare needs will be draining resources from others, making it harder for them to form families.

I should stress that I don't think childcare costs are the big driver of low fertility. But to say that resource reallocation is going to help is a bit ... I mean, where are these resources going to come from? Everyone was already putting their resources towards their families, diverting money away from those families is the engine that powers the state. That is where the soldiers come from, the welfare comes from, all the labour, where the goods get produced, etc. We'd be asking them to stop caring for their families and instead spend all day caring for their families but according to how the government wants instead of what they actually think they need. You can't take from them, give it back to them and expect them to have more. They aren't even going to have the same.