Food pump, i used to use the shell to separate eggs and one out of three yolks would happen to catch on a sharp edge of the shell and break. (I have lots of skills but never was able to get that one). I learned to separate in the hand in a painting materials class in art school in making egg tempera. It was a revelation! So easy, no extra equipment to have (egg separators) and works every time - crack it in the bowl, lift out the yolk, and you can pass it hand-to-hand to get all that coating of white that doesn't come off if you just pass shell-to-shell.
As for sanitary, when you cook something, what is a few residual bacteria after washing going to do? If you cook and eat in sterile conditions you won't have an immune system and it will be so annoying and tiresome you won't enjoy it and will cook less! And are you going to use gloves to knead bread, peel fruit, wash lettuce? I would be more worried about the coating of the gloves giving a bad taste to the food. You touch food all the time, don't they say "il faut mettre la main a la pate"? Not to do, perhaps, if you have a contagious disease but how tedious to cook without using your hands!
In making egg tempera, by the way, since you need the content of the yolk, but not the skin, you then dry your hand (on your pants, obviously, since you're only making paint, but in a kitchen you can use a cloth), pass it to the dry palm, dry the other palm, pass it to the other palm, and back and forth till it's dry enough to pick up with your thumb and forefinger! Then to make tempera, you pierce it with a pin, knife, whatever, and let it drain out.
It;s always fun to show people this.
As for dumping egg white down the drain, i can;t tell you how many jars of egg white have sat in my refrigerator for so long they become archaeological artifacts, having found their way to the far recesses behind old pickle jars and other dubious things. If i'm not planning to bake soon I get real and throw them down the drain. And i bake a lot, but not so much with egg whites.