While I don't quite see how the safety seat alone could cause that much of a difference, I don't think it is unreasonable to see a causal relationship here. Raising a child has gotten more expensive in the US for many reasons (laws about child seats, more money needed for education, no longer socially acceptable to leave kids alone for awhile) and that certainly has an impact.
I'll throw one out there: the birth rate has been falling everywhere across the globe at the same time, even in countries that don't have the same laws about child safety restraints. So the hypothesis is bogus, or it's a tiny fraction of what holistic analysis would suggest are the causes.
It's unreasonable to see causal relationships without rigor, always.
Skepticism is good, but not outright dismissal
The conclusions here are fairly robust because there's a few natural experiments due to different states enacting stricter child safety laws at different times.