It is important to use a hydrating conditioner to replace the sebum layer to protect and hydrate the hair. But there are plenty more reasons to maintain a healthy sebum layer (or bring one back) when it comes to the health of the skin.
Skin Nerves: The nerves associated with the skin are very superficial. If the sebum layer is removed, it often exposes these nerves causing a dry itchy skin which clinically looks the same as allergies, but is not.
Blood Vessels of Skin: If the skin becomes dry due to environmental stress or harsh and/or frequent shampooing without adequate conditioning, the blood vessels will retract to deeper tissue. The body does this to prevent further dehydration from occurring. It actually is a minor form of shock. When a good hydrating conditioner is used the blood vessels will actually come back to the surface. The skin will after even change from a white color to a pink, or even slightly red, color.
Skin Infections: If you do not replace the sebum layer, the skin is more prone to bacteria and fungus (yeast). Furthermore, once the skin becomes dry and starts to crack, the protective barrier is compromised and bacteria, fungus, and allergens now start to move inside.