During his battle against Daz Bones, Zoro was able to sense the breathing of non-living objects, implying those have souls.
The katanas are shown to have some kind of will on their own. The Kitetsu katanas are cursed swords because they kill unworthy people, and Zoro noted that Sandai Kitetsu has a rather wild temper. The way how Ryuma talked about Shusui implied that it also had its own will.
I wonder if Zoro could master them in a way that he’s able to summon the “souls” of his swords. Maybe they could manifest themselves as spirits of previous owners. Zoro said he wanted to become stronger for two people: himself and Kuina.
However, because Kuina is dead, even if Zoro reaches his goal and keeps part of his promise, Kuina herself can’t become the greatest swordsman even if Zoro treats it like he took her place. If Wado Ichimonji actually carries part of Kuina’s soul, she would be able to keep her part of her promise as well and both of them do get stronger at the same time.
*Theory by MajinAkuma
