I think this is the part where there may be a disconnect:
Given that this started in the 1980s the problem will inevitably start to ease off as the elderly come to the end of their lives, although complicated by Japan having one of the longest life expectancies.
The problem is not expected to ease off. Fewer people are being born, in Japan, every year (and people are living longer). The problem isn't expected to ease off but instead to get much worse, quickly. This poses a threat to all areas of the economy (you can't fund pensions or a welfare state if the number of workers is getting smaller every year, and the number of retired people are increasing (as a proportion).
Japan has indeed realized that it is facing economic and potentially societal collapse so, yes, as of last year they invested billions into initiatives to try and boost the birth rate (by easing the financial burden on married couples). In the first year since this investment, the birth rates dropped again, but it'll be interesting to see if they can turn it around.
It's one thing to opt against immigration purely for the sake of growing the economy but, as a working person, I'd prefer to have enough immigration to prevent population decline (which in the UK means net migration of about 0.5m p/a) because it's a choice between having enough immigrants or having more taxes on working people. We're not talking more taxes in the short term, either, but ones that would increase exponentially over time as the population continues to get smaller and older.
Japan's current investment might be too little, too late but at least they are trying to make it financially easier for people to have children. Reform's Thatcherist policies go the other way, so not only would they be slashing immigration but making it economically harder for most people to have families.
I'm not a big fan of the SDP but they at least recognize that, if you want to cut immigration you need to boost birth rates, so are proposing significant financial support to married couples (I think it was $500 per month, per child). They recognize that falling birth rates likely need to be addressed by some degree of wealth distribution. Reform, on the other hand, are going all in on the sorts of policies that have led to declining birth rates in the first place - they would be a disaster for the future of the country.