Learn English – Why doesn’t “king” have an article in “The lion is king of the jungle”

I am learning articles and trying to understand some edge cases.

Help me to decipher the role (the meaning) of articles in this sentence:

The lion is king of the jungle.

1. The lion – is a generic reference to all lions as a class. It can be changed to Lions: Lions are kings of the jungle, the meaning will remain the same.
   • How did I understand it is the generic reference? Because it is the first occurrence of the word lion in the text, but it is preceded by the The article. It suggests the author wasn't implying a specific instance of lion (his pet, for example), but a species in the family Felidae.
   • A lion in this case is valid grammatically, but the meaning will change to "any member of the lion species", not the species as whole.
   • The article about generic nouns.
   • The definite article with a whole class.
2. king of the jungle
   • king – in my opinion this noun should have the the article. Because it is singular and countable, therefore some article is necessary if it is not exception. The a article isn't suitable here, because the king noun is specified by the of the jungle construction: which king? – of the jungle, not any general king. May be the king title doesn't require an article, like breakfast, basketball, etc? But this rule says no – The definite article with titles and positions.
   • the jungle – the same meaning as in the The lion case. Generic reference to all jungles as a class, because it is the first occurrence of the jungle word in the text and has the the article. Also interchangeable with jungles.

Result: Lions (species, general) are the kings (title, specific) of jungles (land cover, general).

Two questions:

1. Is my interpretation correct?

2. Why doesn't king have the the article?

Note – The Oxford Dictionary says: "The lion is the king of the jungle."