On what seems to be one of the finer points of the Japanese mentality.
The means is often more valuable than the end in Japan. Thus:
Take kyuudou (Japanese archery) as an example. The important thing is not hitting the target accurately. It’s things like stance, draw style, demeanor, and attitude—everything you do to prepare for the final (relatively unimportant) step of letting fly an arrow. In the tea ceremony, the goal is not to make delicious tea (although it is delicious). The objective is to prepare the tea according to the particular sect of tea ceremony you follow, and to do so with precise and proper manners. Even the guests at a tea ceremony have a set of manners to follow. As with archery, the final act is subordinate to the preparation. Tennis, though not a traditional sport, is very popular in Japan, perhaps because of the abundance of techniques and rules to master.
In this light, Japanese stories with sad endings (and there are many of them) are perfectly acceptable. Preferred, even—if the characters “do their best” in the run-up to the ending, a sad ending puts even more focus on the main part of the story. “They tried so hard and it didn’t work out the way they hoped.” This forces the audience to think back to what Japanese culture considers the most important part of the story.
Why is it like this and not more like Western culture, a culture obsessed with happy endings? I can’t say—I’ll leave for the real scholars of Japanese society. But I do know it’s been this way for a long time—the love of procedure and sad endings goes back through well more than a thousand years’ worth of Japanese literature and history. Fascinatingly this trend has somehow persisted through today, which is perhaps something that most Western cultures cannot parallel.