It was nearly 2,000 years ago when egg yolk was first mixed with pigments. That seems like a long time ago but there are records of chickens being domesticated for 8,000 years!
There's some chemistry of the drying reactions that still escapes me but I can see the results. My egg and pigment mixtures dry on the palette rather quickly. I've learned to tip the palette to puddle my mix. I'm looking at small and rounded palette wells. This evening I mixed pigment and water but only used a bit with egg. When that was gone, I mixed more.
You see, unlike watercolor, once tempera begins to set up and dry, there is no bringing it back. It's gummy on its way to hard, no longer water soluble.
From The Chemistry of Paints and Painting by Arthur Herbert Church:
"But the yolk of an egg contains other substances besides albumen. First of all, the albumen present is accompanied by another similar compound called vitellin, which closely resembles it in composition and properties, and which, for our present purpose, we need not further describe. Of albumen and vitellin, taken together, egg-yolk contains, as we have seen, not less than 14 or 15 per cent. But egg-yolk is something more than a solution of these two similar bodies. It is, in fact, an oily emulsion, in which innumerable minute globules of a thick, fatty oil are suspended in an albuminous solution. And, moreover, the amount of this oil is large; for there is 30 per cent, of it as against 15 per cent of albumen and vitellin taken together. Hence it happens that egg-yolk, the usual vehicle for pigments in the best kind of tempera-painting, must be regarded as essentially an oil-medium. As it dries, the oil hardens, and remains intimately commingled with the albuminous substances left behind on the evaporation of the water present. These albuminous substances coagulate and become insoluble in the lapse of time—a change greatly accelerated by the old practice of exposing the finished tempera picture to sunshine previous to varnishing it."