"Family life is no longer a core aspiration of every person but becomes a “luxury"..." That is most assuredly not what is happening.
People are just making the best economic investments they can with the time they have. In a low-tech, agricultural society, children are a high value commodity item because workers are high-value commodities. You need workers to get the work done. Agricultural societies are marked by high levels of child labor.
For most of human existence, 5 through 15 year old children worked in the farms and fields. When industry and mining was invented 5-15 year old children worked those in the factories and the coal mines. Children were effectively indentured servants with a ten-year to fifteen-year return. But as the tasks children could do became automated, their economic value disappeared. Children could no longer earn a wage for the family.
In a high-tech, post-industrial society, labor-saving machinery... wait for it... saves labor. As fewer people are needed to get work done, the value of the worker drops. The value of having children drops. It's not that children are a luxury, it's that children are no longer economically valuable. They don't start returning ROI at age 5, as they used to do.
Today, it takes 20 or even 30 years to start seeing return on investment, and the return no longer goes to the family that raised them but to the family they are themselves forming. So, each set of prospective parents sees that they will take a substantial loss on raising children and they... don't.
If children were actually a luxury good, then rich people would have MORE children than poor people do. But that isn't what is happening. Malthus thought children were a luxury good. His original prediction was that rich people would have more children than the poor did. That turned out to be completely wrong. It is fascinating that people invoke Malthus without bothering to have read his theories.
Now, it may observed that those in poverty tend to have more children than the rich. This is a direct result of the welfare state. Because welfare increases payments as a function of marital status and number of children, the welfare state has re-created the pre-industrial ROI children once provided, but it does so only for a particular segment of society instead of society as a whole.
The article linked above notes that Muslim and ultra-orthodox Jews still have large numbers of children, but this is largely due to the economic circumstances they find themselves in. Muslim-predominate countries tend to ether be primarily agricultural or derive their income from oil revenues. Both are essentially pre-industrial. Ultra-orthodox Jews are paid by donors (and sometimes even paid by the Israeli government) to study the Torah. That is, they get the equivalent of government welfare payments for sustenance, as even the author of the article admits in passing:
These ultraorthodox Jews have been enthusiastic clients of Israel’s pro-natalist policies and rely on the support handed out to large families by the state as an economic basis for their traditional lifestyles and their continued study of the Jewish scriptures.
Thus, the article's conclusions about Marx are completely off-base. Insofar as capitalism contains within its demographics the seeds of its own demise, the facts demonstrate Marx was completely clueless. Anyone reading through Marxist writings would search in vain for a reference to the demographics we currently face. Marx had absolutely no idea capitalism would struggle with demography. Asserting that Karl Marx was somehow correct about capitalism is absurd. Marx was simply another Malthus. He was a blowhard, an intellectual who didn't ever really understand how the world works. Failed academics are his tribe, which is why today's failed academics love him so and try endlessly to prop him up as a visionary. Failure calls to failure across the deep, and find consolation in each other.