For me, this framework is not good for the story. We're following characters who aren't believable as people as they go around being one big Deus ex Machina for the islands they visit.
Deus ex Machinas where?
I'm baffled why you want most of the cast to "think and act" like real-life people in a wacky adventure manga targeted towards teenage boys.
There are characters who are believable in the context of this world, but that's boring compared to the silly bubbly main cast.
I know that they often have reasons for why their presence coincides with whatever trouble is happening, but if this is a series of vignette's of the people inhabiting OP's world, then from their perspective the strawhats basically just show up like gods descending from heaven to make the evil dude go away in an unambiguously positive manner.
I mean, I like superhero stories, so it's not like I am utterly against it as a concept of a savior heroes helping out where they go. But if I can't view the characters as actual people and they are indeed depicted as just an ideal, then it just feels like they function as an easy out for the people who need saving.
You have an odd definition of a savior hero. The Straw Hats aren't saviors even though certain circumstances may have their actions overlap into that category. They're not out here to save the world.
This is a plot-driven story where the main heroes, who despite being unruly in their own right, are genuinely good people that will lend a hand to help the downtrodden or a friend in need, but aren't superheroes trying to save the world.
You mention Vivi in the bottom quote, but I think I should remind you that the crew initially helped out Vivi due to being
a) in the wrong place at the wrong time
b) Nami trying to exploit her pleas for money
c) accidentally being targeted on Baroque Works' hit list. It wasn't until after befriending her that they decided to help her regardless.
Not to mention that the people who need saving are rarely interesting or endearing enough for me to want to see them saved.Of all the characters in the series, I think Vivi is the only victim I actually wanted the strawhats to help out. And am alone in that? Do. You guys go into every arc caring about the citizen of whatever, wanting them saved?
For the most part, yes. Because frequently, Oda makes an effort to let the reader get to know a new character and have the reader sympathize with their conflict and plight. Sometimes, having a crisis isn't even necessary to care for a character. Just being relatable and likable is enough.
It doesn't need to be complicated.