From my superficial research on Pinterest (which, to be fair, is all the research I have time for these days) American bakers make something called white cake, which essentially has the same constituent parts as the red velvet (without the cocoa and red colouring, obviously) but added together slightly differently. The main difference is that white cake uses only egg whites.
I tried making this cake the American way without egg yolks, but it always turned out too gummy. I think one needs the emulsifying nature of yolks to keep everything together. So, this is essentially the same as my red velvet recipe, only the butter is replaced entirely with oil and the egg whites are whipped separately for lots of volume.
After baking and cooling, I filled and iced the cakes with the same kind of cooked milk frosting as the red velvet cake. This time, however, I made it by cooking half a pint of milk, 5 teaspoons of cornflour, and 8 ounces of sugar into a custard. I then whipped the custard with 8 ounces of unsalted butter. Cooking the sugar into the custard made for a much nicer mouthfeel. I only used half of this amount of icing for this small cake, before packing the sides with slivered almonds.
Now, was this cake any fluffier than just using the regular recipe and swapping out the cocoa and food colouring? No. Even though this was paler than a normal vanilla butter cake, I have other recipes that would be just as good for making a pale, fluffy sponge.