They proposed some solutions there, but they would rather use a robot in daycare to take care of the children than increase immigration. Something about that seems a little xenophobic and disturbing.
You know in China after they abandoned the one-child policy, they expected a baby-boom. But it did not happen, and they did not expect that social engineering that seemed to fix their immediate problems and increase the income from $200 to about $10 000 per capita would change the very fabric of their society and have a longterm negative effect.
A second child is a liability in the eyes of the people because the cost of living has increased, parents want their child to perform better than themselves and succeed in life for better quality and leap in living standards, so they channel their energy into one child.
I don't see the birthrates increasing in Japan by introducing more women into the workforce while having the same working conditions expecting people to work 80 hours of overtime a month, which also contributes to the weak consumer spending.
I'm sure Japan will solve these problems. They are a first world nation with a highly skilled workforce, so I'm not too pessimistic.