The core does a lot more than keeping the skins apart. The core experiences shear stress when a panel is loaded in bending. The core also provides stability to the skin that is experiencing compression under panel bending.
With thin skinned panels I have tested under bending, the panels always fail on the compression side due to skin buckling when it separates from the core. For a hull, I typically use twice the weight of cloth on the outside as the inside in the panels where the inside will not have any direct load. Simple bending test I have done with H80 core results in skin buckling failure at about half the compressive strength of the fibre. Extra epoxy on the compression side also helps stabilise the fibres to resist buckling.
This short blog has some useful insights and sketches on how composites work:
Rick
It is my understanding the core only needs to keep the skins apart, like an I beam web. This simplification allows us to think of the core only in terms of compressive strength. The horizontal component of the stress is carried by the skins.