"Wonder how much of the spread of blank slatism can be explained by the fact that young people don't have kids anymore"
The other way around. Folk don't have kids (certainly not more than one kid) because they know they'll have great difficulty continuing to believe in the Holy Blank Slate if they have children. Having such a hard disproof - especially one you're exposed to daily - makes it nearly impossible to keep up the pretense.
And that's heresy. You're not a Heretic, are you? Better avoid having kids.