By that I mean, there's not much meat on a mouse or chipmunk, but there's a lot of fur, bones, internal organs, etc. Aren't those considered by-products? It seems like our cats would be adapted to process these parts.
While it's true that cats in the wild eat the whole bodies of their catch (including the heads in some cases), the term " meat by-products" has become a "dirty word" to many cat experts, because of its misuse by some members of the cat food industry. As a result, we have traditionally counseled our readers to avoid all by-products for this reason. (If you get a chance to read Ann Martin's gruesome but eye-opening book, "Food Pets Die For," you will see examples of the sort of things food manufacturers can legally put into their foods under the classification of "meat byproducts."
My opinions about certain byproducts has evolved somewhat since I first wrote the article on Tips for Choosing Cat Food (by the same reasoning process you have used), and I will soon edit that page to reflect those changes.
The founders of the Feline Future web site analyzed the ingredients and nutritional properties of foods cats eat in the wild over a period of a decade or more, and the result was their "recipe" for the Feline Future raw food diet for cats - one which has set the standards for raw feeding, to this day. Actually, they do use a larger proportion of meat to internal organs, so it would appear that part of your premise is incorrect (not much meat on a mouse). In addition, chicken hearts and livers (which are excellent sources of taurine) are added in limited quantities, because of the dangers of "overdosing" with Vitamin A.
In a nutshell, today I would say that a *named* by-product may possibly be acceptable, e.g. " chicken by-product meal" but it should not be listed as the first ingredient in cat food. Unfortunately, labeling laws being what there are, there is no way to my knowledge to know the exact proportion, by weight, of any individual ingredient. Although it is possible to define "protein" as 30% of the product's weight, that protein will include meat, by-products, eggs, certain grains, and other forms of protein in the can or bag of cat food. As a result, I would prefer to see the named by-products relatively far down on the label.
As for the "cheaper brands," unfortunately most of them do contain large amounts of carbohydrate fillers in dry cat food, usually in the form of corn, which is commonly known to be a) difficult for cats to digest and b) implicated in food allergies, probably as a result of "a."
However, in fairness to the "cheaper brands," many premium brands of dry food contain large amounts of carbohydrate fillers. It's the nature of the beast. In the manufacturing process of extrusion (which is a heat-based process), it is necessary to have these dry ingredients in order to effectively shape the dry food nuggets. Some brands of "dry" food do not use grain fillers. Notable examples are listed in Grain-Free Dry Cat Foods, although some of these foods are not carbohydrate-free.