I think the problem is present in all the countries where traditional marriage system has been broken. The only difference between USA and Japan will be that you can find old-homes very easily in USA. Japan being a very conservative country that prides itself over 'protecting' all the bad symptoms of its culture will not solve this problem because, ironically, they think that this is what makes them 'Japanese'.
I don't think it's related to "traditional marriage systems," but instead to social nets and expectations about who will do the caring. For instance, in Scandinavia marriage rates have simply plunged over the last few decades -- fewer and fewer people get married, even though they are still getting together. But social safety nets ensure that taking care of children or older relatives is not such a financial burden as in Japan. Marriage isn't necessary to supporting elders or children in Scandinavia. In Japan, though, there is very little government support. Families are the main line of support, and it is expensive!