Wouldn't extremely generous parental leave be expected to increase the birth rate?
Anyway, if we're talking about spacing 2 - 3 years apart, that means you're not working at all. At some point people will want to go back to work, and that may mean not having another kid.
I think flexible policies are great, but the long leaves I don't think are super useful. Kids are not some abnormal condition; they need to be integrated into a full life.
This is just my pet theory. I think places with overly long leaves (especially overly long paternity leaves) actually discourage men from wanting more children (And of course it takes two to tango here).