You're assuming the birthrate can be "fixed". Japan has an even worse demographic problem. They've tried "fixing" it and nothing much works. Similar for South Korea. Japan would certainly benefit from opening up to more immigration. Countries that can attract more immigration are going to benefit economically as the birthrates continue to decline globally. Why not be attractive to immigrants instead of wanting to repel them?
You're assuming the birthrate can be "fixed". Japan has an even worse demographic problem. They've tried "fixing" it and nothing much works. Similar for South Korea. Japan would certainly benefit from opening up to more immigration. Countries that can attract more immigration are going to benefit economically as the birthrates continue to decline globally. Why not be attractive to immigrants instead of wanting to repel them?