what happens when you whisk sugar with oil?
Oil doesn't really dissolve sugar.  The main purpose for the mixing is that in many recipe techniques, especially the muffin method, sugar is treated as a wet ingredient.  By premixing the wet ingredients, and premixing the dry ingredients, when the two are combined, you require much less additional mixing to get a homogeneous total batter.

Creaming sugar into butter or shortening helps leavening because the sharp edges of the sugar crystals cut air into the solid fat medium, essentially creating a foam.  This then serves as seed air bubbles for the chemical leavening to expand.  This effect cannot occur with liquid oils.

Many carrot cakes are pretty dense and oily, although I don't think they should drip when pressed.  You might have something else going on in your recipes or technique.