Correlation does not equal causation. I feel this study shows correlation, but fails to prove any associated causation.
Maybe people just avoid 3 kids, because it’s hard enough raising one or two kids.
Or cars usually fit 2 child seats because that's the common number they get from customer research.
It is also the number at which your reproduction exceeds that of only replacing your own life. This is very important to some parents to leave the world with more people in it.
A theory that at least is consistent with the observed correlation seems vastly superior to a midbrow dismissal that doesn't. Your "raising kids is hard" theory would explain why people don't have a third child, but raising kids is hard universally. What was observed was that a third child was delayed for longer (even indefinitely) in states with higher age thresholds for mandatory car seats (even when controlling for demographics).
Their causal explanation relies on two additional observations that seem pretty hard to explain by other theories: the effect disappears for single-parent and carless households.