Japan isn't Sweden. It's culture is homogenous and peculiar in a way that few other places even get close to. It's going to be a hard thing for Japan to open it's doors to all the filthy heathens. It's easy to say that all they have to do is open their doors to immigration but even countries like the U.S. that were founded on immigration have a hard time operating in their own interest with a sane and beneficial immigration policy. It's easy and flip and say, "open up the doors," but pretty hard to do when a massive influx of foreigners will massively disrupt a society that's been humming along to it's own tune for most of human history.
To add: Japan is so homogeneously racist that your family can live there for generations and never gain citizenship. There's an entire subculture of Japanese that are considered the lowest of the low because their parents were born overseas in China during the occupation of WWII. To full-blooded Japanese parents. Yamato Japanese account for 86% of Japan's population. 1.6% of Japan's population is ethnically not Japanese. Go to Japan, one in 200 people you meet will be Chinese. One in a thousand will be from the Philippines. Japanese law fully permits Japanese citizens from refusing to hire someone from Okinawa.
I'm not saying allowing immigrants in will solve all issues, or that allowing immigrants in to solve issues is the right reason to allow them in. Allow immigrants in because we are all human beings and we should help each other and see the fact that you have now have more citizens as a bonus.