I think it's because we want a solution to our problems. You can usually find a solution to economic problems.
Cultural problems are nigh impossible to solve- especially by the government.
This is an interesting perspective on the left/right split. People on the left see economic problems (thus government can help), people on the right see cultural problems (thus government will not help).
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.
Economics describes culture. Basically all economic policy recommendations are about "hey, how 'bout a little culture shift toward denser housing, more free trade, less xenophobia when renting out, hiring"
"wanna get a bit more aggregate supply, how about letting women work, maybe even drive!?"
High fertility rates in low income countries are due to factors such as high infant mortality, the participation of children in the labor force, and provision of support for the elderly. Greece's situation, as a middle/high income country, is different.
You can find many countries for each of the permutations of fertility/gdp growth.
Fertility rate is downstream of culture, not economics.