... or rather, more of them? Can't say I have a convincing argument ready for why they should, so I'll just say it's something I'd personally like if they did! Chinese Jian are one possibility (Seiryu uses one), as are European longswords! To my understanding, there's quite a bit of overlap between Katana and Longsword techniques, since they occupied a similar niche and all. I tried to express as much in the recent Weapon Design Contest by submitting some myself, we'll see how that pans out!
I know the job is called Samurai, which conjures up a specific aesthetic, but this is also a sci-fantasy game where swords and magic exist alongside mechas and Star Wars-looking gunships we're talking about. Our character is an adventurer who never stays put for long, so I don't think it feels out of character for them to choose more... unorthodox weaponry, right? They're no longer beholden to any teacher at this point either, having basically outperformed them all. And, at the end of the day, I think we can all agree the odds of them adding another sword DPS are slim to none at this point, so I feel like this isn't too much to ask? They're certainly not shy when it comes to giving others Katana-looking weapons, after all...
All that said, they had the perfect opportunity with Shadowbringers to slip us one or three more unconventional weapons and it either never occurred to them or did, and they chose not to (as the Crystarium Samurai Blade seems to suggest)?
But, hear me out... the First is a parallel world with its own history, and we spend a lot of time in areas such as Lakeland and Voeburt that were shown to have been more traditionally fantasy, with kingdoms and princesses and knights etc. so it's not inconceivable they could've developed and used (two-handed) longswords, as a knightly weapon that maybe never took off on the Source? The First's equivalent of the East is also long gone, so aside from a stray antique or two it kind of made no sense that there would be "katanas" dropping as loot... It's a shame they let the opportunity pass them by, but!
I've noticed they've started referring to SAM weapons as "Samurai Blades" or simply "Blades", which gives me hope that these less specific terms are going to be reflected in the sorts of weapon designs we get, also!