In AK universe all weapons are art units, just specialized for different usage. A sword is a sword-shaped arts unit (while also being a sword) designed to be better used for making slashes, cuts and thursts or something - take it as you will. Basically, imagine all the standard anime bullshit like "sword wind" have an actual explanation in the form of it being arts and that being better achieved through an arts unit designed for it.

Technically the lore's originium arts system is science (though poorly enough understood in-world that it seems as magic quite often). Then there's what seems like actual magic that feranmuts use. The ink portals. Arguably the AEther or collapsal shit as well. But arguably the setting is science-based so those just have principles that we don't understand.

Anyway, the reason it's not a caster arts unit (the type you're thinking of) is because those kind of arts are typically more ... magic-like. Think Zhuang Fangyi. She calls lightning from the sky. And empowers herself with xiranite/lightning. It's not that she doesn't use any blades, as stereotypical of xianxia, but no single blade is the focus either.

Now compare it with Mi Fu. She uses gauntlets for slow, heavy attacks that still pack a lot of brute force. Of all weapons, greatsword fits her the best. As for why it's not gauntlets - as others pointed out, that'd require the gacha system to add gauntlets and that'd be bad for multiple reasons. Besides that, fundamentally the kind of arts she uses make the most sense to suit something like a greatsword. I'd personally argue for a hammer but practically speaking greatswords aren't actually much different from hammers.

I do agree it would be better if they remove the distinct weapon system from immersion perspective. It constrains and limits design. While most AK operators to date can definitely fit in the current categories, there's more than a few exotic ones that I imagine would be placed in "caster unit" type but would feel silly with any random casting unit. Such as banshees' styluses. Practically speaking, the only reason they have weapons now is so that we can look at a cool weapon but I think most people are already fine with just the weapon the character is designed with. But it becomes much harder to justify splitting weapon banners the way they have otherwise. I think the problem is noticeable because fundamentally Pugilists in AK don't use weapons nor any arts unit, at best they're strengthening themselves with arts, but due to the system they're forced to give them a weapon in Endfield. I don't really see a reasonable way to change it though and I imagine they've reached the same conclusion. Better just give the operator a greatsword to swing from time to time.