From what I understand, the 16% is just the industry standard for laying hen feed. Since I have mainly LF, and all of them are heritage, either dual-purpose or meat breeds, I give mine 20% as their regular feed. For the big fall molt, when they are all competing for the most horrifying looking bird, they get tree or four bags (in a row) of 26% to give them a boost to regrow their feathers. Good question, though - I had the same one for a long time before anyone could tell me about the different feeds. I finally met up with a knowledgeable Purina rep, and she helped explain it pretty well. Subsequent conversations over the years with breeders and other feed reps have supported her information.
It is the balance of amino acids rather than crude protein that is important to the hen. The tags are showing the measurement of balanced protein. The hen can use that protein even if it is from a vegetable source. These days, she isn't going to get much in the way of animal protein. It is just too expensive
If the oil is taken out of soybeans, the meal that remains may have 50% protein but that's crude soy protein. The hen can't make use of it without the amino acids that are missing coming to her from somewhere else.
I was curious what the protein level is for cornmeal after corn oil is taken from it. Don't know but if the oil amounts to about half the weight as in soybeans, then an 8% protein corn would become 16% protein defatted cornmeal. Still, you probably couldn't balance the soymeal 50-50 with cornmeal. Coming up with the correct formula is why the animal nutritionist makes the BIG buck, right