Scandinavian countries are commonly listed as a counter-example to what you say. Those countries have strong social safety nets for everyone, and their citizens' basic needs are covered. Child care costs are not an issue for them. Yet, their fertility rates are also too low.
Thus, to the extent that costs and money play a role, it does not seem to be a decisive one. There is something else going on.
Does that include housing? I went and read the Swedish Wikipedia birth rate article (Födelsetal), but couldn't find any clues. Social norms, that's about all.
Presumably the worrying thing here is a possible boom-and-bust cycle. In the long view it should be self-limiting, if a small population with lots of space tends to fill it with a larger future population that then reproduces less. It's just unpleasant to be caught at the declining stage of that cycle, with abundant old people.
Thus, to the extent that costs and money play a role, it does not seem to be a decisive one. There is something else going on.