Yamato "had" to stay in Wano for plot reasons. She wanted to sail the seas during the entire arc, until she was dropped from the nakama roaster at the end. She has no political inclination, other that wanting to see the Dawn Oden spoke about.
If anyone got the mantle of protector of Wano from the outside world, that is Momo, and even in his case, it's less a "keep Wano from being part of the WG" and more of a "don't open the borders until Joy Boy needs it" situation.
Carrot plays second fiddle to Yamato's storyline, where a want for adventure was suddenly curbed by Oda, and the character was relegated into a leadership position unbefitting her up until that moment. Were the WG to attack Zou, of course Carrot would step in to try and defend it. But: the WG has shown no interest toward the elephant nation, nor have they expressed a desire to expand their territories until now with Elbaf; and, considering how Zou fared against Jack's men, I doubt an Admiral invasion would fail.
Loki was portrayed as the foil of his pacifist and WG-aligned father. Loki took to the seas to prove his and Elbaf's might, even if that results in the world's destruction. Loki isn't a protector of Elbaf's culture for stasis reasons: he wants the Country of War to show that they are the best at what they do.
The AK was, as many have speculated through the decades of OP splerging, an all-inclusive continent-spanning political entity. That is an empire by definition. Joy Boy's status as a pirate in no way means that the AK was anarchic, if anything the opposite. For JB to term himself as an outlaw, there first needs to be a law he needs to substract himself to.
And besides, we don't even know what JB's definition of piracy was. Like Luffy, he could have simply pursued an extreme type of freedom, regardless of borders and customs, "bothering" people in power wherever he went.