There are two ways to look at this. Either children are in fact useful for society, and should be subsidized (I weakly hold this view given mass immigration is politically unworkable, and long term that too would run out). That is well and good but cross country data makes the central argument in the title fall apart - US birth rates are/were recently higher than most public healthcare OECD countries. Why blame X if removing X doesn't appear to do much?

The alternative view, that I would hold if it wasn't for the above considerations, is that first world child rearing is currently an expensive hobby, and why should we subsidize it at all? If it wasn't a personal project most would be parents could easily adopt.