I never said that all immigrants are intrinsically a source of problems, and saying that any filtering inevitably leads to never-endingly stronger filters is a slippery slope fallacy.
You absolutely can measure the likely degree of problems an immigrant would bring. To an absurd, extreme, example: you have 1 spot open for immigration. Do you offer it to a semiconductor EE with a clean criminal record in his early 30s, or a 68 year old alcoholic high school dropout with multiple violent criminal convictions?
It's relatively easy to design a system that prioritizes skilled, contributory immigration: academic background, professional career, salary, age, ability to speak the host country's language, skills of relevance, health/fitness, etc.
Sure, the EE from my example can snap and commit a crime, or lose his job and get addicted to drugs; but at a population level, it's inarguable that some groups will cost a country and others will benefit a country.
It's not as if Japan (or any other country, for that matter) doesn't already have immigration restrictions. Japan uses a points-based merit system for permanent residence [1], not unlike the criteria you suggested. Just to give an example, having a PhD and speaking Japanese at an N1 level (~equivalent to B2 CEFR) is barely sufficient to qualify (unless you're older than 30, in which case it won't be).
The more interesting question to ask is: Why has Japan decided to tighten immigration requirements now? But in my opinion the answer is rather obvious, especially when you consider the current Prime Minister's nationalistic beliefs: It's much easier to blame foreigners for insufficient welfare, ailing infrastructure, etc than to actually improve welfare, infrastructure, etc.
Also, the example of "a 68 year old alcoholic high school dropout with multiple violent criminal convictions" is rather ridiculous. You're arguing a strawman. It's already impossible for such a candidate to immigrate almost anywhere barring some other exceptional circumstances.
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[1] See here, eg, to see how you would fare: https://japanprcalculator.com/
The "skilled" immigrant is largely a myth. Many countries now have more graduates than ever before with rising graduate unemployment while these "skilled" immigrants just usually end up being another mediocre tech worker. The GDP per capita hasn't been growing since the crash in 2008 for many European countries despite the influx of "skilled" immigrants.
It is mostly propaganda. Said immigrants will likely still never truly socially fit in even with great effort.