Cultural problems are solvable by government, in the form of propaganda or otherwise. Consider the actions taken by the government against smoking.
By "Otherwise", I will give the example of China and its social credit system that got people to stop spitting in the street by deducting social credit points.
The Chinese government has been pushing propaganda to increase birth rates yet the birth rate keeps declining. If you look at Chinese social media you'll see that modern Chinese young people are making fun of the government propaganda.
Social credit system is not likely to work for as long as the opportunity costs of having kids outweighs whatever punishments the government hands out for not having kids. And in a modern market economy the opportunity cost of having a child is huge indeed.
Cultural change is hard. It is very hard. If it was easy, the USSR would have succeeded in creating the New Soviet Man instead of generations of super cynical people.
People stopped smoking because it's kinda gross, not because of propaganda. Look how much more government propaganda has gone toward eliminating alcohol, weed, and other drugs. People STILL use those drugs, and in some respects they are more popular than ever.
A social credit score only works in an authoritarian regime where you can be hauled off for even slightly criticizing the government. We certainly don't want to resort to anything like that for any problem, as the "solution" is worse.
Alcohol consumption has been falling amongst the young and cigarettes were once considered very fashionable, not at all gross. It was the public health campaigns around lung cancer that changed things.
By "Otherwise", I will give the example of China and its social credit system that got people to stop spitting in the street by deducting social credit points.