I dunno. How invested were the Strawhats in Skypiea? They didn't give a fuck about the backstory of the country- I don't think they actually even know it.
I understand and agree with complaints about them not being on-screen enough, but I'm not so sure about this non-investing stuff.
Arc to arc, off the top of my head
FI- Luffy, Jinbei and Shirahoshi were the heart of the arc, Nami in second due to her background. A good amount of the crew heard the tale of FI and why they were fighting
PH- Chopper and Nami were furious over the treatment of the children, Sanji bonded pretty quick with Kine'mon, Luffy with Momo (I'm going to stop mentioning Luffy from now on, he's always invested)
Dressrosa- Sanji with Viola in his brief time there, Franky told Luffy no matter what he said he was fighting for Kyros and the Tontatta, Ussop became their hero
Zou- all the Strawhats who were there nearly burst into tears after seeing the Mink loyalty. Listened to a part of the Wano story, agreed to go to war
WCI- the arc was about Sanji, obv the Strawhats cared. We also had them bond with the Minks and Pudding
Wano- the arc where we see Zoro finally care about things. A load of them met Yasu and liked him. Ditto for Toko. And this is culmination for all the abuses the Strawhats have seen in PH/Dressrosa/Zou as well, so we do know the Strawhats cared about those things.