A curved sword cuts better, does it not? Japan was lacking steel back in the day, so armor wasn't as prevalent as in Europe. You can't cut armor, so a curved sword wouldn't have been of as much use in Europe. You either overpowered or stabbed. For stabbing, a curve is a disadvantage. However, when firearms started to render armor obsolete, sabers suddenly entered the mainstream in Europe. They are curved because nobody was wearing that much armor anymore. If someone was, they would just make themselves a slower, easier target for a gun.
Sort of? Curving the sword is usually a matter of weight distribution, like I said. That can make it more suited for slashing. Stabbing is pretty much always better at piercing through things that slashing, regardless of if the armor is hardened leather or steel. It just also does less damage, and is more difficult to do in a massed battle, whereas slashing at joints and faces is perfectly viable. Also, spears just tend to do it better than swords. There's a reason swords were often sidearms.
That said, curved swords definitely weren't a product of gunpowder. The seax and falchion both predate the rise of gunpowder weapons by hundreds of years. In fact, while we don't have many physical examples, falchions appear quite frequently in medieval period art, being used by infantry. And curved cavalry swords (like the various swords grouped as "scimitars") are generally used because trying to stab something with a sword from horseback is a bit challenging. The reach just isn't there, unless it's especially long.
Finally, armor wasn't nearly as prevelant in Europe as people seem to think, and when it was used, it was often focused on the upper body. Well made plate armor, while surprisingly wearable and light (the really heavy stuff is mostly heavy because it was effectively sports equipment for jousting), is
expensive.
Not to mention, in Europe, despite steel not being exactly cheap before industrialisation, it was still readily available, so weapons were a bit more a mass production item. Legendary swords in Europe are the kind of Excalibur, whereas in Japan they actually talk about real famous pieces (and they will execute you if you try to smuggle one of those out of the country).
Not true. Up until mass production was possible, swords in Europe were made individually by artisans, many of whom were famous in their times. Areas also tended to have reputations for sword making, like Toledo in Spain. And we
do have examples of existing "legendary" European swords, like Charlemagne's Joyeuse or Saint Ferdinand's Lobera. That you're unfamiliar with them doesn't mean they don't exist.
Nevertheless, why would an isekaied Japanese want to move and fight unlike anyone else, when the locals have for a thousand generations adapted to their particular fantasy world, and their weapons and techniques have adapted with them? If a katana was better, they would already use katanas. It's not like the shape was rocket science.
He wants to fight that way because it's what he can better visualize. It's not because it's superior. And the idea that swords have one "perfect" design is pretty laughable. Smiths in Europe were constantly playing with new designs. That's why the Oakeshott typology for medieval, double edged, one-handed swords alone has 13 different main categories, many of which have subtypes. And that's for one fairly specific category of weapon, across about 500 years of time.
Edit: Also, the shape of the katana comes from the forging techniques used. The form isn't really what's distinctive about katanas. Getting the curve that slight might be a bit tricky with pattern-welded blades, but it could be done.
