Yamato didn’t change idea because she wanted to see the country. Either Oda swiped off countless clues about Yamato joining the Strawhats (I mean, she just declared that she was joining a few chapters ago) with a few badly written lines of dialogue, or he is hiding something happened offscreen between her and Luffy.
I think she is lying, and she is staying to protect Wano (by the way, she might feel it’s her duty because of what her father did to the country). Think about it: Momo fought with an admiral to show that he was able to defend the country. And proved that he had the courage, but not the strength. Momo and the scabbards were losing badly against Greenbull: it was Shanks who made him escape.
Yamato saw this firsthand, and changed her mind about leaving the country. She also knows that, if she says this to Momo, she will shame him: Momo himself told her so. So she spoke with Luffy offscreen, and explained that she wants to stay for as long as it’s needed. Also for the reason that the ancient weapon is there too, so it’ll be ideal to have someone stronger watching after it.
Thus, Luffy gave Momo a flag to protect the country, and Yamato stayed and lied in order to avoid offending Momo: if he knew her real motives, he would literally “order” her to leave.
That’s the reason why Yamato’s change of mind feels cheap: it’s because it’s a lie. She’s making a sacrifice, delaying her adventures for Wano’s sake, but she’s doing it with a smile on her face. This is similar to what Oden did when he agreed to dance naked among the streets: he made a sacrifice and told a lie to everybody for his country’s sake, all the time with a smile on his face.
Vivi also made exactly the same choice, and her choice is one of the most beloved moments of the manga. I wouldn’t be surprised by a later reveal of a Vivi-like moment of Yamato with the crew.
If we look back at Jinbei, he said he wanted to join but couldn’t yet at fishman island. It was over 400 chapter later before he officially joined, but it still happened. I’m sure Oda has a story to tell that involves Yamato being at Wano for some specific purpose we can’t be shown yet.
To be clear, I don’t think there is much evidence for this theory, apart from the fact that Momo and the Scabbards are clearly not able to defend Wano alone. I am only pointing out that, if the theory is true, then the strange behaviour of both the characters and Oda in chapter 1057 makes much more sense.
Luffy clearly stated in the last pages that, as soon as she wants to join, he’ll come back for her.
Tl,dr: Yamato is lying, she is staying to protect Wano, just like Oden pretended to be a fool in order to protect Wano.