Guardian deity is simply a title given to anyone protecting Wano. Kaido, the scabbards, and Luffy have also been referred to as guardian spirits. She's filling up the quota along with them by freeing Wano from Kaido. She can continue doing so after the arc when Luffy claims Wano as his territory.
That's an interesting point.
Well, Yamato's Devil Fruit is linked to a guardian deity of Japan which Wano represents.
That page defines guardian deities as those who protect their liege, the capital, and all of Wano. Sounds like what Yamato could do for future tag team partner Momo and Wano.
And as I stated, Luffy has yet to see Yamato's transformations. Why would Luffy invite Yamato as a crewmate?
Yamato has also been wanting to leave to the seas since she was 8. That's the dream she declared in her Ace flashback and all she's been talking about in the present. Also, she never said anything about aiming to be accepted by Wano citizens. That's just a statement she brushed off from Kaido.
So once Yamato leaves Wano, is the dream complete? That dream seems lacking. What is Yamato's end goal?
Oda's been playing up Ace as her big flashback figure as well if you want to go by that metric. They had a special two-way relationship, he inspired her, and he ended up dying. Checks all the artificial boxes for the SHs.
Ace?! Nah. Ace and Yamato bonded sure but it's not the same. The crewmates are fundamentally affected generally during childhood.
Luffy scarring himself like Shanks, Zoro's dream rivalry with Kuina, Nami money hoarding and taking some of Bellemere's orange trees as momentos, Usopp lying to his mother, Sanji learning to cook from Zeff and experiencing kindness from his mother, Chopper from Hilluik and medicine from Dr. Kureha, Robin learning about Ponegliffs by spying on Professor Clover, Franky building a sea train and ships with Tom, Brook traveling with Yorki and a musical pirate crew, and Jinbe respecting Fisher Tiger since the days of Fish-Man District. I foresee Brook's and Jinbe's childhoods being further explored like Zoro's and Sanji's.
Yamato had Ace's vivre card until Ace died and the stories Ace told Yamato about Luffy. Besides, Luffy had a deeper relationship with Ace than Yamato.
Luffy wasn't interested in recruiting Robin. No starry eyes. No obvious ship role at that time. She invited herself. Is she a guest too?
Hmm...well the invitation/joining process isn't an exact science.
Robin was a mysterious enemy turned ally that snuck on the Merry TWICE, saved Luffy TWICE, and her ship role was immediately explored after Luffy accepted her self invitation. This is after Luffy rescued a suicidal Robin. Luffy decided she was a good person.
Yamato and Luffy lack that type of depth in their interactions. Plus Robin interacted with the Strawhats before joining. Yamato's situation is still a wait and see approach.
Yamato in a way is copying Robin with the self invitation. I don't see Oda doing that again.
She wants to go on adventures similar to what Oden did and Luffy is her best shot at doing that. He's the only one actively going to new islands and has the resources + strength to keep the adventure going.
There are plenty of other adventurers to choose though as you stated Luffy is the best of them. Yamato is un-cuffed and free to do whatever. Yamato does not have to leave Wano when Luffy does. Yamato could wait until Wano's borders are officially open.