Western culture is obsessed with novelty and originality. In the West, one of the worst things you can say about an artist's work is that it's a mere reproduction of something that came before. In Japanese culture, reproduction of classics is held in high esteem. For this reason, the art of creating most of these weapons and using them is still very much alive. Western martial arts and arms rapidly fell into obscurity and oblivion once firearms took over.
Timing may also be a factor. Most western martial arts fell into obscurity and then oblivion centuries ago, while many of these obscure Japanese weapons were still in use well into the nineteenth and even twentieth centuries. Even if Japanese martial techniques had not been valued and maintained, they still would have been in living memory when chambara flicks became popular. For this reason, their portrayal in film has few rivals in Western cinema.
There were a few western martial arts that survived to modern times. Boxing was one, and fencing was another. Fencing certainly had it's heyday, both on the Shakespeare dominated stage and in the golden age of Hollywood thanks to great fencer/actors like Basil Rathbone, but the style of fencing practised was only appropriate to a select few historical settings. Fencing is descended from a duelling discipline and isn't really appropriate in a battle setting or even a fight between commoners. Films where it is appropriate are made so infrequently that actors rarely study fencing at all, let alone enough to become masters.
This is probably why Hollywood embraced Hong Kong fight choreography so enthusiastically in the seventies. It allowed them to fill in the holes left by the death of most Western martial arts with something that was flashy and graceful. Audiences hungry for more Eastern martial arts have naturally consumed a lot of films made in Hong Kong and Japan, and this probably fuelled their curiosity about Japanese weaponry. The fact that Hollywood had to import fight choreography probably also gave many the notion that Eastern martial arts were superior to anything in the West, when the truth is that it was simply better maintained, thanks to cultural values and the relatively late dominance of firearms in the East.