In (fiscal year) 2017, the US admitted 1.1 million immigrants, 1.2 million in 2016. [1] US population has been increasing at about 2.3 million per year [2].
[1] https://www.dhs.gov/immigration-statistics/yearbook/2017/tab...
[2] https://www.multpl.com/united-states-population/table/by-yea...
1) is life expectancy. Suppose the average life expectancy is 40, and every two people have two children at age 20. Population would be stable. However, suppose nothing changes about fertility rates or replacement rates, but the life expectancy grows to say 60. You'll find that the population for some time will grow, merely because inflow (births) don't change, but outflow (deaths) are lower as they are delayed.
As such, population growth can occur despite a below-replacement rate fertility without any immigration.
2) Immigrants tend to be more fertile. Welcoming immigrants and then chalking up the subsequent population growth from their high-birth rate as being an example of the country having sufficiently high birth rates for population growth without immigration is faulty reasoning. Births in the US would've been a lot lower if it admitted no immigrants, particularly hispanic.
Fact is total fertility rates in the US are around 1.7 children per woman now, and are even lower for people who's families have been in the US for multiple generations (non-recent immigrants). US would be declining in population size this century if it wasn't for migration, ceteris paribus.
Similar story all over Europe. Just look at fertility rates of native-born populations and the necessary replacement rate, the former is typically below the latter. [0] Most OECD countries would be shrinking without immigration.
But negative population growth can lead to deflationary systems, and economists are very afraid of those.
In short: if you think you're going to have less customers, you don't invest or hire, and you might layoff, causing further negative data and sentiment, causing further downward pressure on economic activity. 'Death Spiral'. [1]
This is also partly why we keep inflation at 2% target, and not 0%.
[1] https://www.investopedia.com/terms/d/deflationary-spiral.asp
Now, contrast to the current reactionary government of the United States, and their attitude toward immigration. The two countries are clearly moving in opposite directions.
The US is different, of course. People like it here once they've arrived. I can't say why, nor do I buy the stereotype that US culture is more open or individualistic. But the US arguable needs laws quota-based and micro-managey, since they are managing a huge amount of people from more diverse backgrounds. Japan is managing fewer potential immigrants and guests, and most of their immigrants are geographically close to Japan.
Despite the immigration laws being easier to grok and less authoritarian on paper, Japan is pretty strict in its enforcement of those laws. Put all I've said together and I don't know if one country is more reactionary than the other, but I think both countries are moving toward a more balanced, less eccentric immigration system at the moment.
(why you should listen to me: I'm an American and lived in Japan for four years and had to go through the process of getting my wife a spouse visa 2 years into my stay. I dealt with immigration a few times. I went to many different cities and vacations and such, and talked to people that don't speak English and don't have a passport, so I have a representative sample set.)
You’re just making things up now. People are clamoring to get into Japan. It’s one of the safest countries on earth, with one of the highest standards of living. Not to mention inexpensive health care and a surplus of good jobs. I lived there too, and personally saw the people trying to emigrate, from all over the world. And arguing that it used to be different misses the point: they’re becoming more open, and we’re closing off. It’s an indisputable fact.
”The US is different, of course. People like it here once they've arrived. I can't say why, nor do I buy the stereotype that US culture is more open or individualistic.”
If you think US culture is any less difficult to adapt to for an immigrant, you’re incredibly naive. It’s always hard. There’s nothing special about the US, except that we’ve been traditionally willing to accept immigrants. That, itself, is changing, and reactionary douchebags are making it a damned sight more scary and less welcoming by trying to protect the “different” way of life from the scary, scary foreigners.
If I remember well, the visa they get is bound to a specific activity, so for most the only legal way out of that situation will to give up on Japan altogether.