@.access:
Agree with everything up to this point, but it is important to point out one aspect where they are all equal: every SH is not simply a person doing their job, they are (or a meant to become) the best doing their job.
As much as people want to undermine it, the fact Carrot was consistently performing a job during WCI arc is not simply a positive point for her, but unheard of in any of the "special guests". Not a single companion performed a job on the ship. Not Johnny, nor Yosaku, nor Mr. 9, nor Kokoro, nor Chimney, nor Caime, nor Hacchi, nor Pappug, nor Kin'emon, nor Momo, nor Law, nor Kanjuro. Not. a. single. one. Except Carrot. Pedro tried, but the moment he thought of doing it, Carrot went up there and asked for the position. People say this is a regular companion treatment when only SH had that. Go figure.
Of course, one might say this doesn't mean anything, maybe Oda simply thought "know what? I could start making the companions actually be useful and integrate into the crew". That would make sense. But would be a wild guess without any actual weight behind it.
Still, the fact remains so far she can do nothing out of the ordinary with that position. She has shown she could easily be a lookout in any crew and, despite not getting the SH status, she already was the lookout of the crew for an entire arc; but so far she has done nothing to say she can be the SH's lookout.
We could guess she might have some hidden skill that will be shown later, but that would be just another "wild guess without any actual weight".
I agree with you. They are all equally important in the sense that they all work together as one unit to help each other accomplish their dreams. It's sort of the gist of Luffy's speech when fighting Arlong. I fully believe all of their skills will be required and all of their dreams will be interrelated in the final conflict of the series.
I guess I juts meant to say that not all crew positions have received the same time and attention within the narrative. Like the crew sought out people to fill specific positions like chef and doctor and met Sanji and Chopper in the process. Comparatively, Jimbei's position on the crew didn't really receive any particular attention until a scene three quarters of the way through Whole Cake Island after he had already unofficially accepted Luffy's invitation on Fishman Island.
I think you make a very valid point about the consistency with which Carrot filled the same function aboard the ship during WCI. One thing I'd add though is that Zoro, Usopp, and Chopper's arcs sort of rely on them not yet being the best at their respective jobs. Zoro, Usopp, and Chopper all dream of being better or the best and have shown forward progress toward that goal. I'd even say that Sanji was not necessarily demonstrated to be the world's greatest chef in his introductory arc. We're not really told that he's better than say Zeff for example at cooking. We can identify him as a great chef, maybe with greater potential than others and a dream that specifically relates to his skillset.
I'd also argue that we weren't really told Brook was the world's greatest musician either. All we were told was that music was an integral part of his character. His dream isn't really related to being a musician specifically. He just wants to fill a promise to Laboon. We did see Brook become a world famous musician, but that was later, after he joined, over the course of the time skip. In fact, his epitaph, 'Soul King' was also granted after his joining.
I think this contrasts with say Nami, Robin, and Franky who are all preternaturally gifted within their specific fields.