” Why? Because it lowers the value of the yen, which will help their exports “
A ‘cheaper’ yen means lower prices for their exports, sure - but there’s another side to that equation, since Japan IMPORTS virtually all of its raw materials, which means that they will be correspondingly more expensive....
At some point, that congruency squeezes margins so that there is no excess capital left available for rebuilding....
(Or, more likely, I’m not conversant with the nuances, here...)
You are correct that import prices do go up as the yen becomes cheaper. However, in general, Japan makes more money with a cheaper yen than an expensive one. The Bank of Japan has sold a lot of yen over the last 10 years trying to keep the yen cheap against the dollar.
Also, there are ways to mitigate import prices.
The most economical perhaps to own the foreign means of production rather than pay the local market cost for a product; for example, Mitsubishi has mineral resource production around the world. The formula is simple: pay for production and whatever royalty/tax the local government requires instead of paying market prices which get hit directly by the current yen rate.
Japan, for another instance, has enormous oil production despite having virtually no oil reserves.
Instead of paying the world market price for oil, Nippon Oil produces it in foreign markets, pays whatever the local royalty is (usually well below the market price), and refines it in Japan.
This isn't a perfect scheme, of course, since raw resource production is always somewhat chancy; leases can turn out to be dry holes, or the local government increases its demands for royalties or bribes, or production is disrupted by war or natural disaster, or any of a host of other tribulations.
But it also matches the Japanese cultural desire for high quality materials; generally, a Japanese company is happier working with another Japanese company than a foreign one (who knows what kind of dicey product they might be foisting off on you? ;-)