In recent days, the triple world champion has continued to polarise fans with his forays into US politics, fashion, his celebrity status and even veganism.
Yet team boss Toto Wolff said that from Mercedes's point of view, Hamilton's personality is "priceless".
"If he drives a Ferrari road car, he drives a Ferrari road car," he told Speed Week. "You can't lock him in a cage.
"Sometimes it gives us grey hair, but on a difficult day he is the man we want to have in the car."
Marketing boss Jens Thiemer agrees that Mercedes is comfortable with Hamilton's often controversial or polarising views, behaviour and personality.
"We do not want marionettes or robots as ambassadors," he said. "Some personalities are more difficult to handle, but I think to give them too many rules is wrong.
"Drivers must be sensitive to the brand they represent, but you have to let them be themselves as well."
"I liked it, and the fans did too," Thiemer admitted, referring to Hamilton and Rosberg's intense former rivalry.
"I would not say that this season is more boring, as we now have a duel that is not exclusively within the brand."
Wolff also commented: "Our problem with Lewis and Nico was that one was always happy and the other not. Now we have a whole new dynamic.
"The question is what comes next? Do we want to keep this dynamic or is the nuclear variant better for us? I don't know."
Hamilton boasts a 28-point lead over second-placed Sebastian Vettel going into this weekend's Malaysian Grand Prix.