When I look at a lot of recipes, any eggs usually have to be beaten before they're added. If it's all going to be mixed anyway (and well, in dough for example) is it really necessary?
The main purpose of beating an egg is to "denature" the protein within the egg. Proteins are long chains of amino acids and they have lots of internal chemical bonds, which hold them together into tightly contained units. When a protein is denatured, those internal bonds break and the amino acid chains unravel and become elongated. At the same time, atoms that were previously bonded (as part of the internal bonds I mentioned) become available to bond with other molecules.
When an egg is heated to 40 degrees celsius, its protein chains become denatured and elongate, which allows chemical reactions to occur. The egg changes from a liquid solution of protein into a solid mass.
A similar thing happens with you beat an egg. The physical act of beating causes the protein strands to stretch, thereby causing the protein to denature (the internal bonds are broken as a result of the application of physical force). So, rather than the protein chains being bound up into tight balls, they become long strands. This is similar to gluten when it is developed. These strands form structures that allow the trapping of air, which results in a lighter texture.
Beating eggs is not just about mixing. It's about changing the structure of the eggs to produce a physical effect. To read more about this, see "The Science of Cooking" by Peter Barham.
When you cracked the egg and it was in the bowl, you can see that its snuggled together. not mixed.
When beating it, the egg expands which allows the air to be trapped which makes the texture lighter.
This shows that the protein molecules aren't snuggled together but its preformed as an expanded strand egg, which shows the protein molecules every where from small to expanded.
This is about when beating the egg when used as a force called physical.