I want to feed my dog/cat just one protein…. but, that doesn’t really work for them!!

Regarding both cats & dogs ~ because every animal is different (just like people), there is no once size fits all regarding the amount to feed or the protein to feed.  There are guidelines provided by commercial pet food companies (but there are a ton of ingredients in that bag that your animal will never benefit from, and there is little to no quality nutrition to absorb), but you will most definitely want to pay attention to each individual animal.  If you have two cats,  one of your cats likes beef and the other likes chicken, I would not deprive the cat that likes beef from beef and the other from chicken just because feeding only one protein is more convenient.  Different proteins offer different nutrients, and each animal knows what nutrients suite them best.  Trust what your animals are telling you!   Feeding a variety of proteins (because again all proteins are all different and offer different nutrition), offers your animals the best opportunity at a wide range of nutrients.  Animals that eat only one protein are deprived of essential nutrients offered by the other proteins they are not getting.  … eventually, their tastes may change, and you should watch for that, because that is an indication that they are searching for a different nutrient (protein).  Hence, trying to get to ONLY one protein because that would make it convenient (for you), doesn’t really work for them.
The commercial pet food industry USED to tell you to feed only one protein (because they wanted you to return and purchase their product only) wants you to think there is some sort of magical formula for feeding a cat, dog, pig, whatever – do you follow a set prescription for yourself?  Your children?   Carnivores eat meat.  There is no mystery to it.  It is not a chemistry experiment to feed a carnivore.  When an animal is satisfied with the nutrient content, they’ll stop eating, won’t be over weight, won’t have rotten teeth or bad breath, won’t poop volumes, and will most certainly let you know when they would like to be fed again.  When feeding a high quality diet, you don’t need the volume that is suggested on the package of commercial pet food.  You MUST pay attention to your animals size, energy, coat, and interest in the food.