> And as the former die off, and the latter grow - we'll eventually see population growth resume.

Previously (centuries ago) most of the people were like the latter group. And things changed. I would not bet that a group can remain completely unchanged in the next tens to hundreds of years. There is of course a chance, but don't think it is as clear cut as you make it sound.

> Fertility rates also determine age ratios within a society

Plus immigration. Some like and accept that, some hate it and don't like it, we will see how it plays out, but there are more things involved than just fertility rates.

Immigration is largely irrelevant at the current rates of decline for many reasons. A simple one, and without any controversy, is plain old numerics. A shared fertility rate of 1 will trend towards you losing approximately 2.5% of your population per year (which is why Japan's current deterioration will still be seen as the 'good ole days' in their future as they're only losing about 0.5% per year), compounding. So after 80 years, a single human lifetime, your population declines by 87%.

There simply are not enough people to replace this sort of decline, even if you just grab anybody regardless of skills, education, or even the ability to speak your language - which is not exactly a great recipe for a healthy country. Like if 60% of the world, by population, is losing 80% of their population over that timeframe, that'd be a global population decline of 48% with only 40% of people in the rest of the world. You'd need all of them and then a good chunk of their babies too, and that's for less than one human lifetime of change.

I'd say immigration is just kicking the can, but it scarcely even counts as that given how little of an effect it can have even at theoretically absurd levels.

The problem is rates never stay the same. What you say is correct, if nothing changes. But things do change (for one, population is decreasing).

Let me put it another way, if a pandemic would reduce the world population by 50%, what do you think birth rates would do?

Now, if your argument is "it will soon be a shitty time to be old and it will last for a while", with that I do fully agree. The old people of today have it much easier than the old people in 30 years. But people in 80 years might have enough (resources, space, etc.) to start making children again at different rates.

I would say we will live and see, but doubt it is the case for that long periods...

You can't even assume that Amish population growth will remain constant! See e.g. https://medium.com/migration-issues/how-long-until-were-all-.... We also don't know what will happen to Amish retention as the population grows, or what will happen if the population spreads into previously non-Amish areas -- it's just really hard to predict what's going to happen multiple decades in the future.

In general I don't disagree, but more because of the rest of society than the Amish. Every country that's entered into fertility crisis has basically started freaking out and none are anywhere near the worst of it yet. It's only the countries that will be in fertility crisis, but aren't there yet that still have some people think it just comes down to being kind of like now, but with fewer people. I think there's no way the status quo simply continues on. The country to keep an eye on will be China. They're having a catastrophic fertility crisis, have long-term oriented leadership, and have a strong precedent for some fairly batshit means to 'adjust' fertility.

There's also the issue that I don't think I'm a snowflake. Fertility has become a big issue for me and is part of the reason I now have children - not as many as I'd like, but infinitely more than I was thinking about having not that long ago. I've come to view it as a core social responsibility since cultures/societies literally cannot exist without people having enough babies, and I think more people are coming to see it this way as well.