Well, Japan's spiral of depopulation means they actually do need masses of people, and they're importing them too via all sorts of dodgy trainee visas etc to staff convenience stores, hotel front desks, construction sites, lettuce farms etc. It's just politically impossible to support permanent immigration for anybody but the 1%.
The GDP of Japan might benefit, but that doesn't mean benefit for typical Japanese people. Wages would be pushed down. There would be cultural conflict. Japan's unique culture would die.
Japan is not in a permanent spiral of depopulation. There exist families who have plenty of children. These children will tend to do as their parents did. After a few generations of decline, the population will rebound.
Not commenting on your other points, but think you're misguided with this. Culture is not something that stays the same and needs to be preserved; it lives and changes with people. UK today isn't the same it was 30 years ago, and neither is Japan. Trying to set a culture in stone will lead to some quite undesirable undertones.
The tricky thing about depopulation is that it's uneven and has a major time lag. As a simple example, the average Japanese farmer is 67 (!), young Japanese won't do their jobs at any price, and no, you can't just replace them with robots. How do you fix this without immigration or importing all your produce from China?
Japanese culture in 2018 is completely different from the one in 1918, which was again completely different from the one in 1818.
Is the culture currently in an ideal state that needs to be frozen in time? Is immigration a greater threat to Japan than the past experiences of colonialism and nuclear war? If anything, immigration seems ridiculously manageable compared to those.
