It's not actually about orders though, like you said, it's about who's the right hand man. Or rather, who Luffy relies on more, who gets to take more decisions, and who gets to communicate with Luffy when he's not there. Even on the smallest or biggest of scales. Zoro basically gets to do his own thing, and people back him up on it, even Luffy doesn't question him. He's like a second Luffy with green hair and swords as far as his actions within the crew. Zoro is the guy who explained to Chopper why they follow Luffy in Alabasta, and the guy who explained to everyone why Usopp needs to appologise to Luffy. He was in charge of bringing Nami back when Luffy had to stay on Baratie to pay his debt to Zeff. (There is an actual panel where he orders Usopp to come with him). He took it upon himself to KO all of whiskey peak while Luffy was sleeping. He's the only one who deviated from Kinemon's plan and started trouble in Wano and Luffy did the exact same thing the moment he met with him. He's the one Luffy goes to when he needs something done without question: Zoro saving Smoker in Alabasta.
Sanji is a tiny bit less in tune with Luffy, but is still the next best thing. And Sanji and Zoro have great teamwork amongst themselves too.
Franky got to "lead" his own mini-group on Dressrosa, and helped Luffy interogate that one mook outside Doflamingo's casino. He is also the only one who actually tried his luck to get Zoro to call him Aniki lol
Though, tbf, now that I say all this, I have to give Nami and Usopp credit too. Nami runs the ship and Usopp also takes initiative in critical situations without asking permission, like he did with the giants on Enies Lobby and the Tontata on Dressrosa.