Uncle Bob - I really wasn't being sarcastic, that was certainly not my intention. But, I am truly sorry that I said what I did in such a way that you could/would take it as being sarcastic.
Now, to try to answer your questions again - it depends on the application, and the cook's preference.
For baking (bread, pies, etc.), the ratio will affect the gloss and browning. If you are making a pie with a wet filling, like a fruit pie, then you would probably want to use an egg-white wash without liquid to act as a sealer to prevent the bottom crust from getting soggy.
For fried foods like chicken, shrimp, catfish, chicken fried steak, pork chops, etc. (or "oven fried" or baked breaded foods) - the ratio depends on the viscosity you need to hold the outer breading on the food. For something like flour or cornmeal as the outer coating then the wash doesn't need to be too viscous - 1 egg to 1 cup of milk might be just fine - although less milk would also work. For something like course bread crumbs, corn flakes, cracker crumbs, or Panko bread crumbs - you might want a higher ratio of egg to milk to increase the viscosity to hold onto the thicker breading - so 1 egg to 1/4 - 1/2 cup milk might be better. Something else to consider is the milk you use ... buttermilk is more viscous than low-fat 2% milk - so that might influence your decision on the egg:milk ratio.
One other thing that might influence your choice of egg:milk ratio - some people complain about high egg:milk ratio washes tasting "too eggy".
The reason you see various ratios is because there is no one correct answer for any or all applications. When someone writes a recipe they need to "quantify" an amount- so the recipe is just what the person who wrote the recipe used.
Even then, it is not written in stone. My grandmother was from Holly Springs, Grandpa was from down the road in Oxford so I've got a little "Small Town, MS" in my blood, and I never saw her measure the egg:milk ratio when making fried chicken, chicken fried steak, catfish, glazing the top of a pie, etc. ... guess she got it close enough because they were married 55 years and I never heard Grandpa complain about her cooking! Same with my maternal grandmother, who was from Meridian, MS.
