Think of it as mechanical stiffness. Stiffness related to the material properties doesn't change.

Think of a sheet of paper. Try holding it in the air flat. It flops over. Now, put some creases along the length like a fan. Yes, the Moment of inertia does change a little because the paper's overall area on the flat plane might have been slightly shrunk due to the folds, but that is only a factor when the paper is being accelerated, and it would be minuscule. The stiffness of the paper, however, HAS increased. Probably so much so that the paper will remain flat in cantilever. This is the same reason HVAC duct work has small cross-patters in the large flat duct sections. Those indents/creases add stiffness. Also, the reason why many car body panels have "linear design features" along the length of the panels. Form follows function.