In a cake recipe, baking powder is typically used as a leavening agent to provide lift and help the cake rise. While eggs do contribute to the structure and texture of the cake, they are not usually enough on their own to provide sufficient lift. Baking powder contains both an acid and a base, which react when mixed with liquid and heat, producing carbon dioxide gas. This gas creates bubbles in the cake batter, causing it to rise during baking.
In a recipe with a 1:1:1:1 ratio of egg, butter, flour, and sugar, it is likely that baking powder should still be included to ensure proper leavening and a light, fluffy texture. The absence of baking powder may result in a denser, flatter cake, which may not be as desirable.
It's important to follow the recipe instructions precisely to achieve the best results. If a recipe calls for baking powder, it's recommended to include it unless you have a specific reason to make adjustments (e.g., dietary restrictions, alternative leavening methods). If you have concerns about the amount of leavening agent or want to modify the recipe, it's best to consult baking experts or experiment with small test batches before making the full cake.