Quick reference: Choose a binder for structure, leavening for rise, and extra fat or moisture for texture as required by your recipe.
Notes: Some bakes lean on eggs for nearly all of their structure and lift. Where whipped egg is doing the aerating, or where a batter is more egg than flour, no drop-in swap holds the crumb together, and the result collapses or turns dense however carefully the amounts are matched. A recipe built without eggs from the outset is the better starting point than a substitution into one that was not.