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Rather a lot of internet digging hasn't produced much on this question: Why paint FFXiV submersibles, or airships for that matter? It appears that "paint" translates to "dye" - none of which makes a sub any better at much of anything except hiding; which is mostly why they're painted in the real world. Is there any sort of FFXiV game performance boost to having a yellow-polka-dot sub?
Shooter
There is no perks or buffs to painting (dye) the parts of the FC subs or airships.
It is solely an aesthetics / personalization thing.
The dye only effects the major "hull" parts of the individual parts, generally the displayed support structures do not change color.
Commonly, one would dye the sub parts to closer match the FC's crest color set, for example, or to just compliment the FC name or the ship's name.
Of course, no one except who is in the FC or who you have invited into the Company Workshop can see the paint jobs. Only way to further show off or share is by screen shots.
My fleet is painted black ;)
https://i.imgur.com/zoLn5C4.jpg
Some of the most popular things in the game provide no advantage to your character. I'm not certain why you feel this should be different.