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.

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, compounding. This is why Japan's current deterioration will be seen as the 'good ole days' in the future - they're currently "only" losing about 0.5% per year. 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.