While I believe this article to be correct, Germany is an interesting counter-example:

Germany first introduced mandatory child car seat laws on April 1, 1993. [1]

That year, fertility was at 1.28 kids per woman. Since then, it has increased to 1.62.

[1] https://de.wikipedia.org/wiki/Kindersitz

https://www.macrotrends.net/global-metrics/countries/deu/ger...