breading/crumbing: mixing the eggs and flour?

In general, when battering, wet sticks to dry and dry sticks to wet, but they don't stick to themselves.

Thus, if starting with wet food, like meat, the process is usually:

• flour (dry, sticks to the meat, which is wet)
• eggs (wet, sticks to the flour, which is dry)
• crumbs (dry, sticks to the eggs, which are wet)

If you have a wet layer right next to wet food, the batter will fall off during cooking. If you try to stick dry to dry or wet to wet, it just won't adhere well.

You don't need the whole process (you could just use flour and omit the other two layers, for example), but the wet-dry rule is important.

It would be possible to mix (e.g.) eggs and flour to make a wet batter, but that should still be applied to food which is dry. If the food isn't dry, it would need to be floured.

It depends on the final texture you want to achieve. There are tempura recipes that call for flour->batter->breadcrumbs (panko) [thanks @catija!]. You can omit the initial flour layer if you're able to create a dry enough surface for the batter to adhere to. You can even omit the final breadcrumb layer (this is the tempura that I'm used to).

Batters (generally) will result in a relatively thicker (puffier?) coating than the "flour->egg->breadcrumbs" approach. You mentioned chicken wings; usually those are coated in flour (or some sort of starch: potato/corn), fried, and tossed in some sort of sauce. I've seen healthier variations that are roasted or even grilled.

General tips for breading: if you're cooking with friends/family, it's helpful (and fun) to have one person on each station: flour, eggs, breadcrumbs. If you're cooking alone, give yourself plenty of room (large plates), use utensils to help with the initial coating, and keep one hand for dry ingredients (flour and breadcrumbs) and the other hand strictly for the eggs. If you mix up, wash your hands, pat them dry, and continue; otherwise you'll end up with a clumpy mess.

Entirely different texture due to different proportions.

Through standard crumbing technique you're getting an even, thin crusty layer of what is mostly crumbs, with a small amount of egg.

If you make a mix you can dip the meat in, you'll need to use some 3x as much egg, and you get a smooth texture more resembling a corn-dog.

If you mix crumbs and egg in the proportions as they appear on crumbed meat, you'd get a thick dough, not a batter. And it just wouldn't stick to the meat.