What does beating eggs actually do (chemically speaking)?
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.