but why don't we see the "ninja-to" in Koga or Iga ninja houses today? Swords were still made of iron, and since you say there were so cheap that the ninjas didn't care about them, then there should be 100s found around Japan, just left by ninjas. However, we do have many other iron weapons from ninjas in museums, and I am sure those were more cheaply made than a sword.
I don't know any real ninjutsu school in Japan that uses the hollywood style ninja-to
agian please read:"The typical ninjatō carried by a ninja would most likely have been a wakizashi or shortsword fitted with a katana-length handle and placed in a katana-length saya (scabbard). This may have been used to deceive one's opponents into miscalculating how quickly it could be drawn, allowing one to use a battoujutsu strike faster than expected."
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Modern ninjato are often straight with a square tsuba (hand guard), but this is not historically accurate. According to the same book by Masaaki Hatsumi, the ninja ken was straight, but only in contrast to the average sword of the period which were much more curved."
If this "period"
"The Bujinkan dojo currently contains one school, the Togakure ryu, which teaches the use of the ninja ken. Typically, this is a wakizashi-length sword (or slightly longer) that has been outfitted with katana sized koshirae (fittings). The idea behind a shorter sword is that it is much easier to fight in close quarters with a shorter sword, as would be necessary for a ninja acting as an intelligence-gatherer."
correct:
Wakisashi or Ko-katana, sometimes called "ninja-to" or "shinobi-gatana"
incorrect:
ninja-tos, and shinobi-gatanas did exist, but they do not look like what people call "ninja-tos" today.
And the idea that ninjas had straight swords, because they were so cheap, is also wrong because, the ashigaru, the poorest samurai, who were just farmers made into soldiers did not have a straight sword. But if a straight sword is so cheap they should have it right? But ashigaru had wakizashis, uchigatanas, and sometimes katanas. An uchigatana was straighter than the katanas and tachi at the time, but it still looks like a smaller edo-style katana. Ninjas' "ninja-to" is more like an uchigatana.
Ninjas are supposed to be very secretive, so if they were in disguise but they had a straight sword with a large square tsuba, everyone would know he is a ninja. This is another reason why it would be better for a ninja to just have a sword that looks like everyone else's. Even if it is not (shorter blade than usual, in a normal size scabbard). So they can carry around their sword without people knowing he is a ninja.