If a “cooking show” is grammatical, why not a “cooking book”?

Question

I enjoy cooking, and I've been told I'm quite a good cook. I have several cookery books ¹ at home, mostly on Italian and British cooking, but not one is written by a famous cookery writer ². I've never taken a cookery class ³ in my life, but I have learnt a lot from TV cooks such as Jamie Oliver, Nigel Slater and Delia Smith, and I'm an avid fan of their cookery shows ⁴.

In numbers 2, 3, and 4, cookery can be substituted with cooking with no change in meaning, which suggests the two terms are virtually interchangeable. In fact, cookery is the skill or activity of preparing and cooking food while cooking is defined as the activity of preparing or cooking food by Cambridge Dictionaries.

Nevertheless, the best alternative for cookery book is the compound noun cookbook. The instances of cooking book, which Google Ngrams turned up, were vanishingly rare, and mostly, false positives.

American English Ngram chart

British English Ngram chart

Since the 1970s, the expression food writer has superseded that of cookery writer, but cooking writer, although rare, is still used . See Ngram

When a cooking writer pens his autobiography it is invariably written with a freshly baked, rosy glow. Tales of baking at their mother's knee is what is expected.
_{Toast: The Story of a Boy's Hunger by Nigel Slater}

The following graphs clearly illustrate the phenomenal boom of cooking shows, and cookery programmes in the last forty years or so. The BrEng corpus demonstrates that both titles are commonly used...

whereas the AmEng corpus displays a distinct preference for cooking show. The description cookery show barely makes a visible dent on the chart

To sum up, if cooking show, cooking class, cooking skills, and to a lesser extent, cooking writer are all acceptable, what is about cooking book that makes it sound so ‘weird’?

Questions

1. Why is the term cookery rarely used for TV shows and books in American English?

2. Although recipe books are about cooking, these publications are practically never referred to as cooking books. Is there a grammatical or semantic reason for this?

Answer 1

To cook as a transitive verb has the following meaning among many others:

To alter or falsify.

As a slang, it also means to happen as in "What's cooking?" which means "What's happening?"

To cook has some negative connotations especially when it comes to the financial sector or narcotics business.

To cook the books means

to keep false financial records for an organization

I suspect the reason why "cooking book" or "cook book" is not as popular as "cookbook" is the negative connotation of the verb to cook when it is placed before the noun book with a space. I don't think it is a grammatical issue. People have chosen to use "cookbook" as it sounds better.

As for "cooking show", as @Jacinto commented, I don't think it matters that much because the show is about cooking (action) or how to cook food.

Answer 2

Already mentioned is the meaning of "cooking the books," but my first reaction was a visual of book burnings--where people are literally cooking books. There does seem a meaning in "cookbook" of a "cook's book" or "how-to-cook book" layered into the present usage.

As for cookery, I think of a cookie factory when I read or hear it, but I believe it is just a word that isn't in favor (at least in the US)--which seems in-line with your charts.