It has to do with what she represents as a character. What a character thinks they want is superseded by what they actually need. And we'll know what they need upon understanding the character's core. Of which Yamao's appears to be her love of Wano vs her oni blood.
Not the case. She rejected the notion that she'll run Kaido's slave camps for him and continue to persecute the people of Wano on his behalf. She then immediately talked about how she will protect and free them
from Kaido, instead of
for him.
And the primary reason she admires Oden isn't because he went on adventures. It's because he protected Wano and was someone loved by everyone. That's why she claimed she was Oden before she even heard a single word about his adventures.
Her main flashback actually highlighted her love of Wano, its people, and her desire to one day become a warrior citizen too. It was entirely focused around her trying to distance herself from Kaido and pretend to be Oden so that she'd be accepted by the people of Wano. As for the Ace flashback, it's just Tama's rehashed.
Oda also goes out of his way to provide very good reason for characters to leave. In doing so, it's always portrayed as something that's also for the greater good too. Not merely selfish demands. Besides, there are numerous examples of characters choosing their duty over their wishes and being totally happy with that. Oden's own journal details the unspeakable tragedy that befell Wano specifically as a result of abandoning his duty. And in his case, he had an extremely important reason for doing so. Yamao merely wants to roleplay and sightsee.
Right...and yet Yamao is the only one out of all of them to officially have the guardian of wano devil fruit. An immutable characteristic. We're not talking about some passing resemblance like "ah...Luffy looks kinda like that guardian statue thing in this particular form of his many transformations". I mean that her fruit is literally designed entirely with the purpose of being Wano's guardian. The myth that her mythological zoan originates from is very specifically about how the white wolf became a protector in Japan:
https://ralphhaussler.weebly.com/wolf-mythologie-creation-japan-americas-inuit-egypt.html
It's extremely specific and entirely bound to Wano. In the recent SBS we even found out that her club is named "Takeru" further connecting her to his story. As you said, there are many individuals who've been referred to as guardian deities. Yet Oda went the extra mile and had Yamao be the one to actually become the mythological guardian deity.
Her devil fruit
does chain her to Wano, but not in the way you think it does. Obviously she's not just gonna say "Whoops. I ate this guardian df. Guess I've gotta be the guardian then". The point is the very fact that Oda gave her such a devil fruit, is an indication that she's a character that's bound to Wano.
It's extremely common in media to give significant characters abilities that in some way relate to who they are. Powers aren't just plucked out of thin air. The fact that Yamao's ability is inherently Wano bound, therefore suggests the same about her character, since we can see the obvious reason behind her having such a devil fruit. In fact, before we even knew what her fruit was, I was predicting what it would be on the
very basis that it would be some sort of Japanese guardian figure. I was wrong on what specific guardian it was, but my reasoning was spot on, with Oda ultimately choosing something far more specific than even I had in mind. Her fruit isn't some minor inconvenience to just brush to the side...it's
literally who she is as a character.