I have a cake recipe that calls for egg yolks and separately folding in egg whites. What would be the difference in eliminating folding in the whipped egg whites and just using the whole egg? Would it work if I want a "sturdier" cake? That was my thinking but I wasn't certain of the outcome.
I think, as mentioned above, it really depends on how the rest of the recipe goes. If the only source of air youre getting in the cake is from whipping the egg whites then foregoing that may result in very dense cake. However, if there is a step for example that asks you to whisk butter and sugar together until light and fluffy then I think it should be fine to skip it but either way skipping would result in a denser cake.
There are some cakes that call for whipped egg whites but you can opt to skip that step. As an example, a 1-2-3-4 cake wants you to separate the eggs, whip the whites and add them to the completed batter. If you choose not to do that your cake will almost as "sturdy" as a pound cake. But as noted, that would not work with a chiffon cake.