I think it’s because Oda is making the important distinction that Yamato isn’t part of Momo’s retainers. She doesn’t hold an official position in his court like all the Scabbards do.
There’s always been this idea even back when people were theorizing that she would stay behind, that it would be to do so in an “advisory” role for Momonosuke. Some even saying that she would teach him Haki and swordsmanship. Which I always thought was nonsense because Yamato doesn’t know a thing about being a samurai or about swordsmanship, so what could she possible teach him? And also, that’s literally what Kinemon’s role has always been in regards to Momonosuke. But if you pay attention as far back as the raid, Yamato has never had any intention of teaching Momonosuke anything or being a mentor to him. During the raid, instead of helping him figure out how to use the flame clouds, she instead left him to figure it out on his own to attend to other matters she felt were more pressing. When the fighting started, she was all too eager to get out and bust some heads instead of staying behind to protect Momo, whom she ultimately left the task up to Shinobu. She treats him in very much the same way Luffy does, which is for him to stand on his own and figure things out for himself.
And speaking of Luffy, Momonosuke views Yamato as an “outsider” the same way he does Luffy. As in she isn’t from Wano, isn’t a servant of Wano and as such she shouldn’t worry herself about its affairs. It was part of that huge impassioned speech he gave her when he thought she was leaving with Luffy. About how Wano needed to be able to stand on its own two feet and couldn’t keep relying on the kindness of outsiders like her and Luffy. He doesn’t see her as “part of Wano”, like he does his family or the Scabbards. He sees her as a kind friend, but not someone who should be burdened by his country’s affairs.
To me it’s just more confirmation that Yamato’s story obviously doesn’t end in Wano. That’s why he mentioned her as “still learning about the world” and having reassured that even though she was just in a cover story, it doesn’t mean that she won’t be seen again and to look forward to her next appearance.