Yamato's ship role could be many things, until we get further focus on what exactly Yamato can do beyond fighting, certainty remains lacking. (I still want Luffy to get the statue he longs for).
But Yamato's story role within the Straw Hat Pirates appears clear and unique. I'll quote what I stated earlier in the year as I still believe it applies.
@Syphin:
[…]
Yamato may not have been exactly aware of what Roger and Oden were fighting for but once Yamato met Ace and later made the connection between Luffy and Roger and then the connection between Luffy and the presence known as "Joy Boy", did Yamato come to understand the importance of the events to follow (Oden's prediction of the future if he were to fail). When Yamato met Ace, he didn't appear to think much of Oden's prediction about the New Generation and based on its current coverage he did not once consider Ace to be such a figure during their meeting. It was only after that meeting when Yamato had time to process what he learned did he begin to consider Ace as the first and foremost among the pirates Oden was talking about in his journal that would eventually help liberate Wano.
Since then, Yamato has come to appreciate the importance of Wano's borders opening and the need to contribute to the fight that began in the past being waged behind the scenes. Which is why, upon Yamato introducing himself, he immediately expresses his desire to open Wano to the world and to want to fight on Luffy's side because after having read the contents of Oden's journal and having learned about Luffy from Ace, Yamato believes Luffy is the one Roger and Oden were waiting for - the one who will fulfill what Joy Boy set in motion.
From my perspective, unlike other nakama candidates who want to travel with the Straw Hat Pirates because of the adventure, Yamato seeks to travel with the Straw Hat Pirates because of their importance to the battle ongoing over the past 800 years. This is also why Yamato is currently focusing on protecting Momonosuke, who will be a key figure in bringing about the 'Dawn' mentioned in Oden's journal.
Yamato has been presented as a character that can be relevant beyond Wano Kuni. All the developments and plot threads Yamato has been connected with is central to the heart of One Piece's story and mysteries. Oden's journal truly did become a bible for Yamato who has completely cast himself into the destiny that awaits Luffy. I really do expect Yamato to get another flashback during this arc to substantiate what happened when he found out Ace died and began piecing together the connections between the contents of the journal and Luffy. Yamato now likely has a specific reason to want to travel with the Straw Hat Pirates. A reason not currently shared by any other nakama candidate so far introduced (or existing crew member).
And if Oda does script a flashback for Yamato during his battle against Kaido, I am very curious to see if Oda will go back and show how Yamato reacted when he found Ace had died. Could Oda convey Yamato's "3D2Y moment" during that flashback?
@Syphin:
[…]
What if Yamato knew the Straw Hat Pirates would enter the New World two years after the Battle of Marineford? In conjunction with the information contained in Oden's journal where a group of Pirates will appear in Wano twenty years after Oden's death and knowledge of Luffy's dream which echoed what Roger told Oden, if during the conversation Ace and Yamato shared on Onigashima extended to Ace's tattoo and the crossed out "S" it could explain how Yamato was able to decode the message Luffy expressed to his crew. Unlike the Straw Hat Pirates who were aware what the crossed out "3D" meant allowing them to infer a meaning to "2Y", Yamato would be aware what the "2Y" meant when read together with Oden's journal allowing Yamato to infer what the crossed out "3D" could mean. Would not such a development coupled with Yamato's grief over Ace's death and their continual struggles over the past 20 years connect that pain with the Straw Hat Pirates experience from two years ago during the 3D2Y moment? What happens if it is revealed that Yamato made a pledge with themselves as well upon understanding the 3D2Y message - 'when you arrive in Wano Kuni, Luffy, I will be ready to help fight alongside you to stop Kaido and open Wano's borders. And I will set sail with you to experience the world beyond Wano.' (all that Yamato expressed to Luffy when they first met during Yamato's introduction). When Yamato mentioned to Luffy that they were waiting a very long time for him, Yamato may have really been waiting those two years for Luffy.
[…]
If Yamato had decoded the 3D2Y message Luffy left for his crew and has been waiting for Luffy since that day, it would help to establish a connection between Yamato and that intimate moment Luffy and his crew shared. Through Ace, Yamato became involved in the Straw Hat Pirates story and now through the events in Wano Kuni, Yamato is becoming closely associated to the Straw Hat Pirates adventure. The foundation Oda is setting up with Yamato being aware of Luffy's dream and his relevance to the "One Piece" is not just window dressing. There is a deeper meaning to Oda having Yamato being closely connected to the end goals of One Piece and the mysteries surrounding it.