Baking without eggs fails most often because the egg is treated as one ingredient to be replaced. It is doing at least four distinct jobs, and each has to be covered separately.
The protein network is the main loss
Egg proteins unfold in heat and link into a mesh that traps air and gives a bake its structure once cooled, which is what stops a cake from being a dense pudding.
Nothing common in a kitchen reproduces that mesh directly, so egg-free baking builds structure from starch and flour protein instead, which set differently and less firmly.
This is why Indian sweets and many traditional egg-free bakes are dense, syrup-soaked or set by fat and reduction rather than trying to be light in the same way.
Emulsification has to be replaced deliberately
Egg yolk contains natural emulsifiers that hold fat and water together in a batter, keeping the mixture smooth rather than allowing it to separate during mixing and baking.
Without them a batter can split, and split batters bake unevenly, with fat pooling and the crumb turning greasy in patches.
Yoghurt, condensed milk, nut pastes and certain plant milks bring their own emulsifiers, which is why egg-free recipes so often specify one of these rather than plain water.
Lift has to come from chemistry or air
Whipped eggs incorporate air mechanically and hold it, providing a large share of the rise in many cakes before any raising agent contributes.
Removing them means the lift must come from bicarbonate reacting with an acid, from steam, or from creaming fat and sugar hard enough to trap air in the fat.
Acid ingredients therefore appear frequently in egg-free recipes, since they are the trigger the raising agent needs and also tenderise the crumb.
Moisture and richness are a separate problem
Eggs are largely water but they carry that water bound within protein and fat, so it is released slowly during baking rather than evaporating immediately.
Replacing them with plain liquid gives a batter that dries out faster, which is why egg-free bakes stale noticeably sooner unless something binds the water.
Fruit purees, milk solids and starches hold moisture in the crumb, which is the practical reason they appear in these recipes far more than in conventional ones.
The best results redesign rather than substitute
Recipes written from the start without eggs tend to work better than conversions, because the ratios of flour, liquid, fat and sugar have all been rebalanced together.
A conversion changes one variable in a formula that was tuned around it, and the other four ingredients are then in the wrong proportion for what remains.
Traditions with long-standing egg-free sweet making are the most useful reference, since they solved these constraints without ever treating the egg as the default.