On top of incorrect projections, I also think most don't understand the math of how fertility rates affect populations. It's an exponential system, so extreme outcomes are entirely possible with rates that seem 'bad' but not that bad, like e.g. a fertility rate of 1. Such a fertility rate, if shared among an entire population, would result in an exponential 50% decline in your population per 20 years. And alongside that you get social chaos, screwed up age ratios, economic chaos, and more. All on an extremely rapid timeframe.
I think this is a self correcting problem, but it's likely far wiser to fix it before it starts fixing itself.
My fear is the correction will involve rolling back women’s rights.
In fact when you look at any typical modern fertility correlation explanation, they all really just fall apart under the slightest of scrutiny. Education/income stuff? Look at Thailand - extremely low education, extremely low income, extremely low fertility - even lower than Japan! So what is the real driving factor? It seems clear that if people believe 'true happiness' is just one 'thing' away, then they are motivated to continue chasing those things. Children don't really have a place in this sort of world - as they simply imperil your ability to pursue that sort of perceived happiness. And governments and companies alike have every motivation in the world to push this 'thing based' worldview, consumerism in other words, because it generates income, increases GDP, and so on.
This is the only fertility correlate that explains literally everything in a clean and consistent fashion. For instance the bell curve of income:fertility (very poor and very rich have far more children than the middle class) can be easily explained - both the very poor and very rich are unable to participate in consumerism. The former because of too little money, the latter because they have too much. Thailand? Yes, it's very poor yet there is also rampant consumerism at all levels, and it's even a place when walking into the most mainstream mall in the capitol you're immediately greeted with a literal lambo dealership. And so on for the countless other issues and counter-examples that contemporary fertility correlates fail to explain.
[1] - https://en.wikipedia.org/wiki/List_of_countries_by_tertiary_...
I imagine if we were consuming news from India, Egypt or Nigeria it would be a very different story.