I don't think that's really the concern.

The concern is that most developed economies are essentially a ponzi scheme where the workers are taxed to support the children, those on benefits and the older members of society.

People will support that system to some degree, because they contribute to it while they're working, with the promise of a state pension or other benefits when they are older (I realise as writing this that this is quite a Euro-centric and socialist mindset).

The problem these countries are facing once the population declines is that the population as a whole is older on average. Sure, some old people will be dying, but if the rate of births falls below the death rate, then inevitably, the average age of the population increases. This means that more of the population as a percentage will be receiving benefits from the state, and the cost of that is borne by the decreasing percentage of the population that is working.

This is more than just pensions and socialist benefits though, even in an extreme hypothetical country with no tax and no benefits at all, and aging population still places an increased consumption demand on a smaller workforce that can produce goods to satisfy that demand. Such an economy will necessarily have to shift their trade balance more towards importing goods to maintain the same standard of living. A smaller workforce is also likely to have a lower GDP.

The falling birthrate also becomes important, because any policies to try to reverse the trend also have a massively delayed effect on the economy. A falling birthrate now means a huge problem in 20-60 years time when the effect will be felt in the working population. Likewise, any policies to incentivise couples to have children will take 20 years to benefit the economy. If the problem isn't addressed now, it will be too late.

The reason the baby boomer generation has been so successful is because the working population massively outnumbered the population needing to rely on benefits.

I'm assuming of course, that we think that a decreasing GDP or "standards of living" are a bad thing. Most people would say yes, but maybe the reality is that the baby boomer generation have just had it too good.

Population levels have been at crisis levels for a while now, with a global population now that's double that of 50 years ago or 4 times that of 100 years ago. Our capacity to keep producing food can't keep increasing at that rate, and huge numbers of people live in overcrowded conditions. Even more significant is that access to fresh water is at a near critical level in many places, and there have been predictions that future wars might well be triggered by fighting to secure access to drinking water.

The current predictions are that global population will peak at 10 billion (another 25% above now) in another 50 years and start dropping off. That means that all of the things above will get worse over the next 50 years - even more overcrowding, less food, less access to drinking water, as well as worsening GDP and ability to maintain the same standard of consumption as before. Perhaps only after we see a massive collapse in global population can we start existing more sustainably as a species again.